Pub Date : 2004-12-01DOI: 10.1109/CDC.2004.1429508
M. Lazar, W. M. Heemels, S. Weiland, A. Bemporad
Model predictive control (MPC) has recently been applied to several relevant classes of hybrid systems with promising results. These developments generated an increasing interest towards issues such as stability and computational problems that arise in hybrid MPC. Stability aspects have been addressed only marginally. In this paper we present an extension of the terminal cost and constraint set method for guaranteeing stability in MPC to the class of constrained piecewise affine systems. Semidefinite programming is used to calculate the employed terminal weight matrix that ensures stability for quadratic cost based MPC. A procedure for computing a robust positively invariant set for piecewise linear systems is also developed. The implementation of the proposed method is illustrated by an example.
{"title":"Stabilization conditions for model predictive control of constrained PWA systems","authors":"M. Lazar, W. M. Heemels, S. Weiland, A. Bemporad","doi":"10.1109/CDC.2004.1429508","DOIUrl":"https://doi.org/10.1109/CDC.2004.1429508","url":null,"abstract":"Model predictive control (MPC) has recently been applied to several relevant classes of hybrid systems with promising results. These developments generated an increasing interest towards issues such as stability and computational problems that arise in hybrid MPC. Stability aspects have been addressed only marginally. In this paper we present an extension of the terminal cost and constraint set method for guaranteeing stability in MPC to the class of constrained piecewise affine systems. Semidefinite programming is used to calculate the employed terminal weight matrix that ensures stability for quadratic cost based MPC. A procedure for computing a robust positively invariant set for piecewise linear systems is also developed. The implementation of the proposed method is illustrated by an example.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126125345","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 : 2004-12-01DOI: 10.1109/CDC.2004.1429625
N. Elia, Jeff N. Eisenbeis
In this paper we investigate control across stochastic drop-out channels. We seek optimal linear controllers and receivers for mean-square stability that make use of the knowledge of whether a packet is received. We establish a fundamental bound on drop-out probability allowable for stabilization. The main result is a remote stabilization technique that always achieves this bound via acknowledgement from the actuation receiver. Controller information structure and decentralization issues are considered as they may further limit the achievable performance.
{"title":"Limitations of linear remote control over packet drop networks","authors":"N. Elia, Jeff N. Eisenbeis","doi":"10.1109/CDC.2004.1429625","DOIUrl":"https://doi.org/10.1109/CDC.2004.1429625","url":null,"abstract":"In this paper we investigate control across stochastic drop-out channels. We seek optimal linear controllers and receivers for mean-square stability that make use of the knowledge of whether a packet is received. We establish a fundamental bound on drop-out probability allowable for stabilization. The main result is a remote stabilization technique that always achieves this bound via acknowledgement from the actuation receiver. Controller information structure and decentralization issues are considered as they may further limit the achievable performance.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122241133","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 : 2004-12-01DOI: 10.1109/CDC.2004.1429398
D. Chatterjee, D. Liberzon
In this paper we propose a method for stability analysis of switched systems perturbed by a Wiener process. It utilizes multiple Lyapunov-like functions and is analogous to an existing result for deterministic switched systems.
{"title":"On stability of stochastic switched systems","authors":"D. Chatterjee, D. Liberzon","doi":"10.1109/CDC.2004.1429398","DOIUrl":"https://doi.org/10.1109/CDC.2004.1429398","url":null,"abstract":"In this paper we propose a method for stability analysis of switched systems perturbed by a Wiener process. It utilizes multiple Lyapunov-like functions and is analogous to an existing result for deterministic switched systems.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131592943","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 : 2004-12-01DOI: 10.1109/CDC.2004.1428932
Chung-Wei Cheng, M. Tsai, J. Maciejowski
This paper presents a feedrate-controlled interpolator for accurate feedrate control of CNC machine tools along NURBS curves for precision CNC machining. Unlike most existing interpolators, usually based on the Taylor expansion, the proposed method uses an Adams-Moulton predictor-corrector algorithm instead. An upper bound on the sampling interval is established, which guarantees convergence of the corrector iterations (within each interval). Experimental results are presented to demonstrate the effectiveness of the proposed interpolator for machining curved paths defined by NURBS.
{"title":"Accurate feedrate control of CNC machine tools along NURBS curves","authors":"Chung-Wei Cheng, M. Tsai, J. Maciejowski","doi":"10.1109/CDC.2004.1428932","DOIUrl":"https://doi.org/10.1109/CDC.2004.1428932","url":null,"abstract":"This paper presents a feedrate-controlled interpolator for accurate feedrate control of CNC machine tools along NURBS curves for precision CNC machining. Unlike most existing interpolators, usually based on the Taylor expansion, the proposed method uses an Adams-Moulton predictor-corrector algorithm instead. An upper bound on the sampling interval is established, which guarantees convergence of the corrector iterations (within each interval). Experimental results are presented to demonstrate the effectiveness of the proposed interpolator for machining curved paths defined by NURBS.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115718763","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 : 2004-12-01DOI: 10.1109/CDC.2004.1429512
M. Margaliot, D. Liberzon
We present a stability criterion for switched nonlinear systems which involves Lie brackets of the individual vector fields but does not require that these vector fields commute. A special case of the main result says that a switched system generated by a pair of globally asymptotically stable nonlinear vector fields whose third-order Lie brackets vanish is globally uniformly asymptotically stable under arbitrary switching. This generalizes a known fact for switched linear systems and provides a partial solution to the open problem posed by Liberzon (2004). To prove the result, we consider an optimal control problem which consists in finding the "most unstable" trajectory for an associated control system, and show that there exists an optimal solution which is bang-bang with a bound on the total number of switches. By construction, our criterion also automatically applies to the corresponding relaxed differential inclusion.
{"title":"A Lie-algebraic condition for stability of switched nonlinear systems","authors":"M. Margaliot, D. Liberzon","doi":"10.1109/CDC.2004.1429512","DOIUrl":"https://doi.org/10.1109/CDC.2004.1429512","url":null,"abstract":"We present a stability criterion for switched nonlinear systems which involves Lie brackets of the individual vector fields but does not require that these vector fields commute. A special case of the main result says that a switched system generated by a pair of globally asymptotically stable nonlinear vector fields whose third-order Lie brackets vanish is globally uniformly asymptotically stable under arbitrary switching. This generalizes a known fact for switched linear systems and provides a partial solution to the open problem posed by Liberzon (2004). To prove the result, we consider an optimal control problem which consists in finding the \"most unstable\" trajectory for an associated control system, and show that there exists an optimal solution which is bang-bang with a bound on the total number of switches. By construction, our criterion also automatically applies to the corresponding relaxed differential inclusion.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"244 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121892450","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 : 2004-12-01DOI: 10.1109/CDC.2004.1428804
S. Prajna, A. Jadbabaie, George J. Pappas
We develop a new method for safety verification of stochastic systems based on functions of states termed barrier certificates. Given a stochastic continuous or hybrid system and sets of initial and unsafe states, our method computes an upper bound on the probability that a trajectory of the system reaches the unsafe set, a bound whose validity is proven by the existence of a barrier certificate. For polynomial systems, both the upper bound and its corresponding barrier certificate can be computed using convex optimization, and hence the method is computationally tractable.
{"title":"Stochastic safety verification using barrier certificates","authors":"S. Prajna, A. Jadbabaie, George J. Pappas","doi":"10.1109/CDC.2004.1428804","DOIUrl":"https://doi.org/10.1109/CDC.2004.1428804","url":null,"abstract":"We develop a new method for safety verification of stochastic systems based on functions of states termed barrier certificates. Given a stochastic continuous or hybrid system and sets of initial and unsafe states, our method computes an upper bound on the probability that a trajectory of the system reaches the unsafe set, a bound whose validity is proven by the existence of a barrier certificate. For polynomial systems, both the upper bound and its corresponding barrier certificate can be computed using convex optimization, and hence the method is computationally tractable.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121525041","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 : 2004-12-01DOI: 10.1109/CDC.2004.1428934
D. Materassi, M. Basso, R. Genesio
The paper deals with harmonic balance analysis of tapping mode atomic force microscopes. The separation-amplitude curve is analytically evaluated for a large class of common tip-sample interaction potentials. The proposed approach provides an useful insight of many nonlinear known phenomena with respect to fully numerical approaches.
{"title":"Frequency analysis of atomic force microscopes with repulsive-attractive interaction potentials","authors":"D. Materassi, M. Basso, R. Genesio","doi":"10.1109/CDC.2004.1428934","DOIUrl":"https://doi.org/10.1109/CDC.2004.1428934","url":null,"abstract":"The paper deals with harmonic balance analysis of tapping mode atomic force microscopes. The separation-amplitude curve is analytically evaluated for a large class of common tip-sample interaction potentials. The proposed approach provides an useful insight of many nonlinear known phenomena with respect to fully numerical approaches.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127008042","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 : 2004-12-01DOI: 10.1109/CDC.2004.1430263
Daron Acemoglu, A. Ozdaglar, R. Srikant
We consider the problem of resource allocation in a wireless network operated by a single service provider. The motivating model is the downlink in a cellular network where the provider sets the price of entry into the wireless network and then allocates power levels (and transmission rates) to the participating users as a function of the users' channel conditions according to a pre-specified policy. The provider's goal is to design the power allocation policy that maximizes its revenue, recognizing the effects of his decisions on the choice of users to join the network. We show that the power allocation policy chosen by the service provider satisfies the following marginal user principle: the network allocates power levels such that the utility of the marginal user, who is indifferent to joining the network or not, is maximized. While the motivation is drawn from power allocation, the marginal user principle also generalizes to other resource allocation problems.
{"title":"The marginal user principle for resource allocation in wireless networks","authors":"Daron Acemoglu, A. Ozdaglar, R. Srikant","doi":"10.1109/CDC.2004.1430263","DOIUrl":"https://doi.org/10.1109/CDC.2004.1430263","url":null,"abstract":"We consider the problem of resource allocation in a wireless network operated by a single service provider. The motivating model is the downlink in a cellular network where the provider sets the price of entry into the wireless network and then allocates power levels (and transmission rates) to the participating users as a function of the users' channel conditions according to a pre-specified policy. The provider's goal is to design the power allocation policy that maximizes its revenue, recognizing the effects of his decisions on the choice of users to join the network. We show that the power allocation policy chosen by the service provider satisfies the following marginal user principle: the network allocates power levels such that the utility of the marginal user, who is indifferent to joining the network or not, is maximized. While the motivation is drawn from power allocation, the marginal user principle also generalizes to other resource allocation problems.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126388848","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 : 2004-12-01DOI: 10.1109/CDC.2004.1428650
Jinglai Shen, A. Sanyal, N. Chaturvedi, D. Bernstein, H. Mcclamroch
New pendulum models are introduced and studied. The pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force and control forces and moments. Several different pendulum models are developed to analyze properties of the uncontrolled pendulum. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the spherical 2D pendulum models as special cases. The case where the rigid body is asymmetric and the center of mass is distinct from the pivot location leads to the 3D pendulum. Rigid pendulum and multi-body pendulum control problems are proposed. The 3D pendulum models provide a rich source of examples for nonlinear dynamics and control, some of which are similar to simpler pendulum models and some of which are completely new.
{"title":"Dynamics and control of a 3D pendulum","authors":"Jinglai Shen, A. Sanyal, N. Chaturvedi, D. Bernstein, H. Mcclamroch","doi":"10.1109/CDC.2004.1428650","DOIUrl":"https://doi.org/10.1109/CDC.2004.1428650","url":null,"abstract":"New pendulum models are introduced and studied. The pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force and control forces and moments. Several different pendulum models are developed to analyze properties of the uncontrolled pendulum. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the spherical 2D pendulum models as special cases. The case where the rigid body is asymmetric and the center of mass is distinct from the pivot location leads to the 3D pendulum. Rigid pendulum and multi-body pendulum control problems are proposed. The 3D pendulum models provide a rich source of examples for nonlinear dynamics and control, some of which are similar to simpler pendulum models and some of which are completely new.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125839054","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 : 2004-12-01DOI: 10.1109/CDC.2004.1428837
D. Bauso, L. Giarré, R. Pesenti
In this paper, a team of n unmanned air-vehicles (UAVs) in cooperative path planning is given the task of reaching the assigned target while i) avoiding threat zones ii) synchronizing minimum time arrivals on the target, and iii) ensuring arrivals coming from different directions. We highlight three main contributions. First we develop a novel hybrid model and suit it to the problem at hand. Second, we design consensus protocols for the management of information. Third, we synthesize local predictive controllers through a distributed, scalable and suboptimal neuro-dynamic programming (NDP) algorithm.
{"title":"Multiple UAV cooperative path planning via neuro-dynamic programming","authors":"D. Bauso, L. Giarré, R. Pesenti","doi":"10.1109/CDC.2004.1428837","DOIUrl":"https://doi.org/10.1109/CDC.2004.1428837","url":null,"abstract":"In this paper, a team of n unmanned air-vehicles (UAVs) in cooperative path planning is given the task of reaching the assigned target while i) avoiding threat zones ii) synchronizing minimum time arrivals on the target, and iii) ensuring arrivals coming from different directions. We highlight three main contributions. First we develop a novel hybrid model and suit it to the problem at hand. Second, we design consensus protocols for the management of information. Third, we synthesize local predictive controllers through a distributed, scalable and suboptimal neuro-dynamic programming (NDP) algorithm.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128091350","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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