Automation and Remote Control最新文献

We consider some problems with a set-valued mapping, which can be reduced to minimization of a homogeneous Lipschitz function on the unit sphere. Latter problem can be solved in some cases with a first order algorithm—the gradient projection method. As one of the examples, the case when set-valued mapping is the reachable set of a linear autonomous controlled system is considered. In several settings, the linear convergence is proven. The methods used in proofs follow those introduced by B.T. Polyak for the case where Lezanski–Polyak–Lojasiewicz condition holds. Unlike algorithms that use approximation of the reachable set, the proposed algorithms depend far less on dimension and other parameters of the problem. Efficient error estimation is possible. Numerical experiments confirm the effectiveness of the considered approach. This approach can also be applied to various set-theoretical problems with general set-valued mappings.

The problem of finding the arrangement of closed-loop control system poles that minimizes an objective function is considered. The system optimality criterion is the value of the H_∞ norm of the frequency transfer function relative to the disturbance with constraints imposed on the system pole placement and the values of the H_∞ norm of the sensitivity function and the transfer function from measurement noise to control. An optimization problem is formulated as follows: the vector of variables consists of the characteristic polynomial roots of the closed loop system with the admissible values restricted to a given pole placement region; in addition to the optimality criterion, the objective function includes penalty elements for other constraints. It is proposed to use a logarithmic scale for the moduli of the characteristic polynomial roots as elements of the vector of variables. The multi-extremality problem of the objective function is solved using the multiple start procedure. A coordinate descent modification with a pair of coordinates varied simultaneously is used for search.

This paper is devoted to the problem of solving a system of nonlinear equations with an arbitrary but continuous vector function on the left-hand side. By assumption, the values of its components are the only a priori information available about this function. An approximate solution of the system is determined using some iterative method with parameters, and the qualitative properties of the method are assessed in terms of a quadratic residual functional. We propose a self-learning (reinforcement) procedure based on auxiliary Monte Carlo (MC) experiments, an exponential utility function, and a payoff function that implements Bellman’s optimality principle. A theorem on the strict monotonic decrease of the residual functional is proven.

An adaptive state-feedback control system is proposed for a class of linear time-varying systems represented in the controller canonical form. The adaptation problem is reduced to the one of Taylor series-based first approximations of the ideal controller parameters. The exponential convergence of identification and tracking errors of such an approximation to an arbitrarily small and adjustable neighbourhood of the equilibrium point is ensured if the condition of the regressor persistent excitation with a sufficiently small time period is satisfied. The obtained theoretical results are validated via numerical experiments.

In this paper, stationary random processes with fuzzy states are studied. The properties of their numerical characteristics—fuzzy expectations, expectations, and covariance functions—are established. The spectral representation of the covariance function, the generalized Wiener–Khinchin theorem, is proved. The main attention is paid to the problem of transforming a stationary fuzzy random process (signal) by a linear dynamic system. Explicit-form relationships are obtained for the fuzzy expectations (and expectations) of input and output stationary fuzzy random processes. An algorithm is developed and justified to calculate the covariance function of a stationary fuzzy random process at the output of a linear dynamic system from the covariance function of a stationary input fuzzy random process. The results rest on the properties of fuzzy random variables and numerical random processes. Triangular fuzzy random processes are considered as examples.

For a linear time-varying singularly perturbed system with a small parameter μ for a part of derivatives and quasi-differentiable coefficients, existence conditions are established and μ-asymptotic composite full- and reduced-order observers are constructed. The error in estimating a state with an arbitrary predetermined exponential decay rate converges to an infinitesimal value of the same order of smallness as the small parameter. The observer gain vector are expressed in terms of the gain vectors of subsystems of smaller dimension than the original one and independent of the small parameter, and the parameters of the original system are subject to weaker requirements than those previously known. A constructive algorithm for calculating the gain vector of a composite observer is presented.

A dynamic measuring system is considered. A new model of the measuring system, a method for processing of measurement results and a method of restoring the input signal of the system by the noisy output signal are proposed. The estimation of the accuracy of the method and a computational experiment demonstrating the efficiency of the signal recovery method are presented.

Stability of a switching system, which comes to existence when stabilizing a chain of two integrators by a feedback in the form of nested saturators, is studied. The use of the feedback in the form of nested saturators makes it possible to take into account boundedness of the control resource and to ensure the fulfillment of the phase constraint on the velocity of approaching the equilibrium state, which is especially important in the case of large initial deviations. A Lyapunov function is constructed by means of which global asymptotic stability of the closed-loop system is proved for any positive feedback coefficients.

This paper continues previous studies on designing stabilizing control laws for a mechanical system consisting of a wheel and a pendulum suspended on its axis. The control objective is to simultaneously stabilize the vertical position of the pendulum and a given position of the wheel. The difficulty of this problem is that the same control is used to achieve two targets, i.e., stabilize the pendulum angle and the wheel rotation angle. Previously, the output feedback linearization method was applied to this problem. The sum of the pendulum angle and the wheel rotation angle was taken as the output. For the closed loop system to be not only asymptotically stable in the output but also to have asymptotically stable zero dynamics, a dissipative term was added to the output-stabilizing control law. Below, a two-parameter modification of this law is described. Along with the dissipative term, we introduce a positive factor. The more general parameterization allows stabilizing this system in the cases where the control law proposed previously appeared ineffective. The properties of the new control law are investigated, and the attraction domain is estimated. The estimation procedure is reduced to checking the feasibility of linear matrix inequalities.

The problem of constructing reachable and null-controllable sets for stationary linear discrete-time systems with a summary constraint on the scalar control is considered. For the case of quadratic constraints and a diagonalizable matrix of the system, these sets are built explicitly in the form of ellipsoids. In the general case, the limit reachable and null-controllable sets are represented as fixed points of a contraction mapping in the metric space of compact sets. On the basis of the method of simple iteration, a convergent procedure for constructing their external estimates with an indication of the a priori approximation error is proposed. Examples are given.