Pub Date : 1988-06-15DOI: 10.23919/ACC.1988.4790114
G. Huang, T.S. Tang
For the optimal control problem of a nonlinear distributed parameter system (DPS) with an index constainnig partial differential operators in the spatial variables, deriving a costate system equation and the associated boundary and final conditions in component notations is very tedious and complicated. Matrix methods, which provide structural and operational convenience, are introduced into the derivations. The costate system with the final condition for a class of DPS's and indices consisting of the first order partial differential operator is given in a compact matrix form.
{"title":"Applying Matrix Methods to Optimal Control of Distributed Parameter Systems","authors":"G. Huang, T.S. Tang","doi":"10.23919/ACC.1988.4790114","DOIUrl":"https://doi.org/10.23919/ACC.1988.4790114","url":null,"abstract":"For the optimal control problem of a nonlinear distributed parameter system (DPS) with an index constainnig partial differential operators in the spatial variables, deriving a costate system equation and the associated boundary and final conditions in component notations is very tedious and complicated. Matrix methods, which provide structural and operational convenience, are introduced into the derivations. The costate system with the final condition for a class of DPS's and indices consisting of the first order partial differential operator is given in a compact matrix form.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86906776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1988-06-15DOI: 10.23919/ACC.1988.4790021
Jianxin Tang, P. Luh, T. Chang
This paper studies static optimization with equality constraints by using the mixed coordination method. The idea is to relax equality constraints via Lagrange multipliers, and creat a hierarchy where the Lagrange multipliers and part of the decision variables are selected as high level variables. The method was proposed about ten years ago with a simple high level updating scheme. In this paper we show that this simple updating scheme has a linear convergence rate under appropriate conditions. To obtain faster convergence, the Modified Newton's Method is adopted at the high level. There are two difficulties associated with the Modified Newton's Method. One is how to obtain the Hessian matrix in determining the Newton direction, as second order derivatives of the objective function with respect to all high level variables are needed. The second is when to stop in performing a line search along the Newton direction, as the high level problem is a maxmini problem looking for a saddle point. In this paper, the Hessian matrix is obtained by using a kind of sensitivity analysis. The line search stopping criterion, on the other hand, is based on the norm of the gradient vector. Extensive numerical testing results are provided in the paper. Since the low level is a set of independent subproblems, the method is well suited for parallel processing. Furthermore, since convexification terms can be added while maintaining separability of the original problem, the method is promising for nonconvex problems.
{"title":"Optimization with the Mixed Coordination Method","authors":"Jianxin Tang, P. Luh, T. Chang","doi":"10.23919/ACC.1988.4790021","DOIUrl":"https://doi.org/10.23919/ACC.1988.4790021","url":null,"abstract":"This paper studies static optimization with equality constraints by using the mixed coordination method. The idea is to relax equality constraints via Lagrange multipliers, and creat a hierarchy where the Lagrange multipliers and part of the decision variables are selected as high level variables. The method was proposed about ten years ago with a simple high level updating scheme. In this paper we show that this simple updating scheme has a linear convergence rate under appropriate conditions. To obtain faster convergence, the Modified Newton's Method is adopted at the high level. There are two difficulties associated with the Modified Newton's Method. One is how to obtain the Hessian matrix in determining the Newton direction, as second order derivatives of the objective function with respect to all high level variables are needed. The second is when to stop in performing a line search along the Newton direction, as the high level problem is a maxmini problem looking for a saddle point. In this paper, the Hessian matrix is obtained by using a kind of sensitivity analysis. The line search stopping criterion, on the other hand, is based on the norm of the gradient vector. Extensive numerical testing results are provided in the paper. Since the low level is a set of independent subproblems, the method is well suited for parallel processing. Furthermore, since convexification terms can be added while maintaining separability of the original problem, the method is promising for nonconvex problems.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86489605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1988-06-15DOI: 10.23919/ACC.1988.4789822
S. Phillips, R. Kosut, G. Franklin
An averaging analysis of indirect, discrete-time, adaptive control systems is presented. The analysis results in a signal dependent stablity condition and accounts for unmodeled plant dynamics as well as exogenous disturbances. This analysis is applied to two discrete-time adaptive algorithms: An unnormalized gradient algorithm and a recursive least squares algorithm with resetting. Since linearization and averaging are used for the gradient analysis, a local stability result valid for small adaptation gains is found. For RLS with resetting, the assumption is that there is a long time between resets. The results for the two algorithms are virtually identical emphasizing their similarities in adaptive control.
{"title":"An Averaging Analysis of Discrete-Time Indirect Adaptive Control","authors":"S. Phillips, R. Kosut, G. Franklin","doi":"10.23919/ACC.1988.4789822","DOIUrl":"https://doi.org/10.23919/ACC.1988.4789822","url":null,"abstract":"An averaging analysis of indirect, discrete-time, adaptive control systems is presented. The analysis results in a signal dependent stablity condition and accounts for unmodeled plant dynamics as well as exogenous disturbances. This analysis is applied to two discrete-time adaptive algorithms: An unnormalized gradient algorithm and a recursive least squares algorithm with resetting. Since linearization and averaging are used for the gradient analysis, a local stability result valid for small adaptation gains is found. For RLS with resetting, the assumption is that there is a long time between resets. The results for the two algorithms are virtually identical emphasizing their similarities in adaptive control.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86074350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1988-06-15DOI: 10.23919/ACC.1988.4789793
K. Passino, P. Antsaklis
Artificial Intelligence planning systems determine a sequence of actions to be taken to solve a problem. This is accomplished by generating and evaluating alternative courses of action. A special type of Petri net is first defined and then used to model a class of Artificial Intelligence planning problems. A planning strategy is developed using results from the theory of heuristic search. In particular, the A* algorithm is utilized. From the Petri net framework it is shown how to develop an admissible and consistent A* algorithm. As an illustration of the results three Artificial Intelligence planning problems are modelled and solved.
{"title":"Artificial Intelligence Planning Problems in a Petri Net Framework","authors":"K. Passino, P. Antsaklis","doi":"10.23919/ACC.1988.4789793","DOIUrl":"https://doi.org/10.23919/ACC.1988.4789793","url":null,"abstract":"Artificial Intelligence planning systems determine a sequence of actions to be taken to solve a problem. This is accomplished by generating and evaluating alternative courses of action. A special type of Petri net is first defined and then used to model a class of Artificial Intelligence planning problems. A planning strategy is developed using results from the theory of heuristic search. In particular, the A* algorithm is utilized. From the Petri net framework it is shown how to develop an admissible and consistent A* algorithm. As an illustration of the results three Artificial Intelligence planning problems are modelled and solved.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86094503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1988-06-15DOI: 10.23919/ACC.1988.4789752
B. Chang, S. Banda
This paper generalizes Chang and Pearson's computation of optimal H∞ norm to the case with multiple right-half-plane zeros. Sarason's interpolation theory is used to reduced the problem to a simple eigenvalue or singular value computation.
{"title":"Optimal H∞ norm computation for MIMO systems with multiple RHP zeros","authors":"B. Chang, S. Banda","doi":"10.23919/ACC.1988.4789752","DOIUrl":"https://doi.org/10.23919/ACC.1988.4789752","url":null,"abstract":"This paper generalizes Chang and Pearson's computation of optimal H∞ norm to the case with multiple right-half-plane zeros. Sarason's interpolation theory is used to reduced the problem to a simple eigenvalue or singular value computation.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90506825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1988-06-15DOI: 10.23919/ACC.1988.4789824
Scot Morrison, B. Walker
The stability robustness of an indirect adaptive control algorithm using batch least squares identification is examined. By enforcing a persistence of excitation condition on the reference input, a bound on the parameter estimation errors due to the unmodelled dynamics is developed. Conditions under which the closed loop stability of a pole-placement adaptive control strategy can be expected are then developed from this bound using Kharitonov's theorem. The stability robustness of the algorithm is tested on two simulation examples, one of which includes very lightly damped unmodelled dynamics.
{"title":"Batch Least Squares Adaptive Control in the Presence of Unmodelled Dynamics","authors":"Scot Morrison, B. Walker","doi":"10.23919/ACC.1988.4789824","DOIUrl":"https://doi.org/10.23919/ACC.1988.4789824","url":null,"abstract":"The stability robustness of an indirect adaptive control algorithm using batch least squares identification is examined. By enforcing a persistence of excitation condition on the reference input, a bound on the parameter estimation errors due to the unmodelled dynamics is developed. Conditions under which the closed loop stability of a pole-placement adaptive control strategy can be expected are then developed from this bound using Kharitonov's theorem. The stability robustness of the algorithm is tested on two simulation examples, one of which includes very lightly damped unmodelled dynamics.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91424188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1988-06-15DOI: 10.1109/ACC.1988.4173049
P. L. Shaffer, T. Johnson
The amount of concurrency which is inherent in an engine control algorithm, and a methodology for computing this measure based on existing programs, are presented. The control is partitioned into functional blocks, followed by analyses of data dependencies and of execution time. Concurrency is increased by modification and decomposition of bottleneck functions. For the control program analyzed, exploitation of concurrency at the function level allows a reduction of execution time to 15% of the sequential execution time. This paper reports work originated by GE and continued there in accordance with the USAF Future Advanced Control Technology Study (FACTS) [1].
{"title":"Data Flow Analysis of Concurrency in a Turbojet Engine Control Program","authors":"P. L. Shaffer, T. Johnson","doi":"10.1109/ACC.1988.4173049","DOIUrl":"https://doi.org/10.1109/ACC.1988.4173049","url":null,"abstract":"The amount of concurrency which is inherent in an engine control algorithm, and a methodology for computing this measure based on existing programs, are presented. The control is partitioned into functional blocks, followed by analyses of data dependencies and of execution time. Concurrency is increased by modification and decomposition of bottleneck functions. For the control program analyzed, exploitation of concurrency at the function level allows a reduction of execution time to 15% of the sequential execution time. This paper reports work originated by GE and continued there in accordance with the USAF Future Advanced Control Technology Study (FACTS) [1].","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83022760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1988-06-15DOI: 10.1109/ACC.1988.4172997
R. Bartusiak, C. Georgakis, M. J. Reilly
Reference system synthesis, an equation-based method for designing nonlinear feedforward/feedback controllers for general dynamic systems is presented. The control objective is expressed as a desired closed loop behavior in the form of a set of integro-differential equations which can, by design, be nonlinear. Realization of the desired closed loop behavior depends upon the solution of an operator equation relating the open loop system to the desired closed loop system for computing the necessary manipulated variable action. Analytical solutions of this operator equation can be found for simple systems. In general, numerical solutions can be determined using Newton's method, for example. The advantages of reference system synthesis are (i) it provides a general method for designing nonlinear feedforward/feedback controllers, (ii) it is simple, and (iii) its loop-shaping capabilities allow for the design of deliberately nonlinear closed loop behavior for higher performance and constraint-avoiding control. In this paper, we introduce the reference system synthesis procedure, illustrate its application to simple dynamical systems, and discuss the relationship of reference system synthesis to PID and Internal Model Control design procedures.
{"title":"Designing Nonlinear Control Structures by Reference System Synthesis","authors":"R. Bartusiak, C. Georgakis, M. J. Reilly","doi":"10.1109/ACC.1988.4172997","DOIUrl":"https://doi.org/10.1109/ACC.1988.4172997","url":null,"abstract":"Reference system synthesis, an equation-based method for designing nonlinear feedforward/feedback controllers for general dynamic systems is presented. The control objective is expressed as a desired closed loop behavior in the form of a set of integro-differential equations which can, by design, be nonlinear. Realization of the desired closed loop behavior depends upon the solution of an operator equation relating the open loop system to the desired closed loop system for computing the necessary manipulated variable action. Analytical solutions of this operator equation can be found for simple systems. In general, numerical solutions can be determined using Newton's method, for example. The advantages of reference system synthesis are (i) it provides a general method for designing nonlinear feedforward/feedback controllers, (ii) it is simple, and (iii) its loop-shaping capabilities allow for the design of deliberately nonlinear closed loop behavior for higher performance and constraint-avoiding control. In this paper, we introduce the reference system synthesis procedure, illustrate its application to simple dynamical systems, and discuss the relationship of reference system synthesis to PID and Internal Model Control design procedures.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80771248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1988-06-15DOI: 10.1109/ACC.1988.4172939
Chia-Chi Tsui
This note shows that in computing the feedback gain for eigenvalue assignment in multivariable systems, the reduction of the condition number of the closed loop eigenvector matrix (CLEM) is a necessary step to achieve some highly important and desirable technical and computational properties. This note also shows that the reduction of the condition number of other relevant matrix does not sufficiently imply the achievement of these properties. The only existing algorithm capable of reducing the condition number of CLEM computes the explicit CLEM. Fortunately, this computation is very efficient and numerically stable, and is completely different from the computation of the eigenvector matrix of a given matrix.
{"title":"On The Computation Of Eigenvalue Assignment Problem","authors":"Chia-Chi Tsui","doi":"10.1109/ACC.1988.4172939","DOIUrl":"https://doi.org/10.1109/ACC.1988.4172939","url":null,"abstract":"This note shows that in computing the feedback gain for eigenvalue assignment in multivariable systems, the reduction of the condition number of the closed loop eigenvector matrix (CLEM) is a necessary step to achieve some highly important and desirable technical and computational properties. This note also shows that the reduction of the condition number of other relevant matrix does not sufficiently imply the achievement of these properties. The only existing algorithm capable of reducing the condition number of CLEM computes the explicit CLEM. Fortunately, this computation is very efficient and numerically stable, and is completely different from the computation of the eigenvector matrix of a given matrix.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79677315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1988-06-15DOI: 10.23919/ACC.1988.4789734
V. Mukhopadhyay
This paper presents a formulation for synthesis of digital active control laws for aeroservoelastic systems, which are typically modeled by large order equations in order to accurately represent the rigid and flexible body modes, unsteady aerodynamic forces, actuator dynamics, and gust spectra. The control law is expected to satisfy multiple design requirements on the dynamic loads, responses, actuator deflection and rate limitations, as well as maintain certain stability margins, yet should be simple enough to be implemented by an onboard digital microprocessor. The synthesis procedure minimizes a linear quadratic Gaussian type cost function, by updating selected free parameters of the control law, while satisfying a set of inequality constraints on the design loads, responses and stability margins. A stable classical control law or an estimator based full or reduced order control law can be used as an initial design starting point. The gradients of the cost function and the constraints, with respect to the digital control law design variables are derived analytically, to facilitate rapid convergence. Selected design responses can be treated as constraints instead of lumping them into the cost function, in order to satisfy individual root-mean-square load and response limitations. Constraints are also imposed on the minimum singular value requirements for stability robustness improvement.
{"title":"Digital Active Control Law Synthesis for Aeroservoelastic Systems","authors":"V. Mukhopadhyay","doi":"10.23919/ACC.1988.4789734","DOIUrl":"https://doi.org/10.23919/ACC.1988.4789734","url":null,"abstract":"This paper presents a formulation for synthesis of digital active control laws for aeroservoelastic systems, which are typically modeled by large order equations in order to accurately represent the rigid and flexible body modes, unsteady aerodynamic forces, actuator dynamics, and gust spectra. The control law is expected to satisfy multiple design requirements on the dynamic loads, responses, actuator deflection and rate limitations, as well as maintain certain stability margins, yet should be simple enough to be implemented by an onboard digital microprocessor. The synthesis procedure minimizes a linear quadratic Gaussian type cost function, by updating selected free parameters of the control law, while satisfying a set of inequality constraints on the design loads, responses and stability margins. A stable classical control law or an estimator based full or reduced order control law can be used as an initial design starting point. The gradients of the cost function and the constraints, with respect to the digital control law design variables are derived analytically, to facilitate rapid convergence. Selected design responses can be treated as constraints instead of lumping them into the cost function, in order to satisfy individual root-mean-square load and response limitations. Constraints are also imposed on the minimum singular value requirements for stability robustness improvement.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79689779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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