Reachabilty sequences of minimal length for discrete-time switched linear control systems

For the deterministic case, a linear controlled system is alwayspth order stable as long as we use the control obtained as the solution of the so-called LQ-problem. For the stochastic case, however, a linear controlled system with multiplicative noise is not alwayspth mean stable for largep, even if we use the LQ-optimal control. Hence, it is meaningful to solve the LP-optimal control problem (i.e., linear system,pth order cost functional) for eachp. In this paper, we define the LP-optimal control problem and completely solve it for the scalar case. For the multidimensional case, we get some results, but the general solution of this problem seems to be impossible. So, we consider thepth mean stabilization problem more intensively and give a sufficient condition for the existence of apth mean stabilizing control by using the contraction mapping method in a Hilbert space. Some examples are also given.

Matrix quadratic equation solution derivation applied in finding steady state solutions of Riccati differential equations with constant coefficients

The paper continues the authors’ study of the linearizability problem for nonlinear control systems. In the recent work (Sklyar, Syst Control Lett 134:104572, 2019), conditions on mappability of a nonlinear control system to a preassigned linear system with analytic matrices were obtained. In the present paper, we solve more general problem on linearizability conditions without indicating a target linear system. To this end, we give a description of invariants for linear nonautonomous single-input controllable systems with analytic matrices, which allow classifying such systems up to transformations of coordinates. This study leads to one problem from the theory of linear ordinary differential equations with meromorphic coefficients. As a result, we obtain a criterion for mappability of nonlinear control systems to linear control systems with analytic matrices.

For the last five decades, there has been great interest in the control literature in deriving reduced order models for large-scale linear control systems. Such reduced order models have great applications in science, engineering and industry. In this paper, we have studied the problem of designing linear functional observers for large-scale linear discrete-time control systems and derived some new results, viz. necessary and sufficient conditions for the reduced order linear functional observer for discrete-time linear control systems. We have also established a separation principle for implementation of an observer-based feedback stabilization scheme. A simple algorithm has been provided for the ready implementation of the proposed linear functional observer. A numerical example using MATLAB has been provided to illustrate the new design procedure.

The authors reconsider and advance the analysis of controllability and observability (and the weaker stabilisability and detectability properties) of a class of linear networked control systems (NCSs). The authors model the NCS as a periodic system with limited communication where the non-updated signals can either be held constant (the zero-order-hold case) or reset to zero. Periodicity is dealt with the lifting technique. The authors provide conditions for controllability (stabilisability) and observability (detectability) of the NCS, given a communication sequence and the controlled plant model. These conditions allow to find communication sequences which are shorter than previously established. A strict lower bound for the sequence length is given. In the sampled-data case, the authors prove that a communication sequence that avoids particularly defined pathological sampling rates and particular eigenvalues can preserve stabilisability (and detectability for the dual problem) with a ‘minimum’ sequence length.

Invited Papers.- Nonlinear H-infinity control theory: A literature survey.- Primitives for robot control.- Optimal frequency design vs. an area of several complex variables.- Feedback stabilization of nonlinear systems.- Multivariable Feedback.- A monotonicity result for the periodic Riccati equation.- Results on generalized Riccati equations arising in stochastic control.- LQ-Problem: The discrete-time time-varying case.- The output-stabilizable subspace and linear optimal control.- The decomposition of (A,B) invariant subspaces and its application.- The set of feedback matrices that assign the poles of a system.- Model matching for linear Hamiltonian systems.- Connective stabilization of large-scale systems: A stable factorization approach.- Riccati equations, algebras, and invariant systems.- Maximal order reduction of proper transfer function matrices.- The matching condition and feedback controllability of uncertain linear systems.- Convergence properties of indefinite linear quadratic problems with receding horizon.- Robust Control.- Generalized stability of linear singularly perturbed systems including calculation of maximal parameter range.- Convex combinations of Hurwitz functions and its applications to robustness analysis.- Designing strictly positive real transfer function families: A necessary and sufficient condition for low degree and structured families.- Quadratic stabilizability of linear systems with structural independent time varying uncertainties.- A finite zero exclusion principle.- Design of controller with asymptotic disturbance attenuation.- H-infinity Control.- Gas turbine control using mixed sensitivity H-infinity optimisation.- Nonlinear H-infinity Theory.- A J-spectral factorization approach to H-infinity control.- Vector interpolation, H-infinity control and model reduction.- Sensitivity minimization and robust stabilization by stable controller.- Conjugation and H-infinity control.- Necessary and sufficient conditions for the existence of H-infinity con trollers: An interpolation approach.- On H-infinity contro4 LQG control and minimum entropy.- Optimal H-infinity SISO-controllers with structural constraints.- Super optimal H-infinity design.- H-infinity control with state feedback.- Adaptive Control.- Convergence analysis of self-tuning controllers by Bayesian embedding.- On bounded adaptive control with reduced prior knowledge.- Indirect techniques for adaptive input output linearization of nonlinear systems.- Stochastic Control and Filtering.- Interpolation approach to the H-infinity filter problem.- Stochastic disturbance decoupling.- Discrete-time filtering for linear systems in correlated noise with non-Gaussian initial conditions: Formulas and asymptotics.- Nonlinear Control.- Boundary feedback stabilization of distributed parameter systems.- Optimal nonlinear feedback system design for a general tracking problem.- Stability theory for differential/algebraic systems with application to power systems.- Feedback equivalence of planar systems and stabilizability.- Topological dynamics of discrete-time systems.- Another approach to the local disturbance decoupling problem with stability for nonlinear systems.- Stabilization of nonlinear systems and coprime factorization.- Observability and Identification of Nonlinear Systems.- Identification of linear systems via Prony's method.- On observability of chaotic systems: an example.- Interpolating uniquely with only a finite class of polynomials.- Sinc approximation method for coefficient identification in parabolic systems.- Observability and Harish-Chandra Modules.- Robotics.- Modelling and nonlinear control of an overhead crane.- On adaptive linearizing control of omnidirectional mobile robots.- Robot control via nonlinear observer.- Modelling and simulation of flexible beams using cubic splines and zero-order holds.- Towards a differential topological classification of robot manipulators.- An adaptive PD control algorithm for robots.- Robustness of Infinite-Dimensional Systems.- Comparison of robustness measures for a flexible structure.- Robust stabilization for infinite-dimensional linear systems using normalized co-prime factorizations.- Standard problem for distributed systems.- Robust stabilization of delay systems.- Topological aspects of transfer matrices with entries in the quotient field of H-infinity.- On the Nyquist criterion and robust stabilization for infinite-dimensional systems.- Real stability radii for infinite dimensional systems.- Robust stability condition for infinite-dimensional systems with internal exponential stability.

This paper studies the general output observation problem for linear infinite-dimensional control systems with bounded input and output operators. Both, the plant and the observer are described by state space models with linear, unbounded system operators, generating strongly continuous semigroups. The plant has two inputs and two outputs. One input is for control, available to the observer, and the other for disturbance. In turn, one output is for the so-called measured signal, available to the observer, and the other for the so-called output to be observed. Using knowledge of the control and the measured output the observer output is to asymptotically follow the output to be observed and that condition is called the output observation. Disturbances are generated by a homogeneous, linear system with an unknown initial condition. Some sufficient conditions for the output observation are derived. These conditions involve the plant, observer and disturbance system operators and consist of two linear operator equations with one of them being an algebraic Sylvester equation. We show that the obtained conditions are constructive and under the assumption on the exponential detectability of the plant allow to derive a design procedure for the output observer. The presented results extend those for linear finite-dimensional control systems.

On the local-global decomposition of linear control systems

Nonlinear aeroservoelastic analysis of a controlled multiple-actuated-wing model with free-play

ABSTRACTIn this paper, we study invariant control systems that generalise positive systems. A characterisation of linear control systems invariant on polyhedral cones (corner regions) in the state-space, called cone-invariant linear control systems, is established both for the inputs taking values in a polyhedral cone in the control space and for the inputs taking values in an affine polyhedral cone. The problem of equivalence between control systems invariant on corner regions is introduced. For cone-invariant linear control systems, we study invariance-preserving state-equivalence and invariance-preserving feedback-equivalence and present characterisations of both notions of equivalence.

Aspects concerning the design of linear and fuzzy control systems based on the Iterative Feedback Tuning (IFT) approach are discussed. Two types of controller parametric conditions are derived to guarantee the robust stability of the control systems. The conditions are included in the steps of the IFT algorithms of linear control systems. Next an IFT-based design of a class of Takagi-Sugeno PI-fuzzy controllers (PI-FCs) is given. The design method maps the parameters of the linear PI controllers onto the parameters of the Takagi-Sugeno PI-FCs. The application of IFT in linear and fuzzy control systems is exemplified in a case study dealing with the angular position control of a DC servo system with backlash laboratory equipment. The performance enhancement ensured by IFT and fuzzy control is illustrated by real-time experimental results.KeywordsIterative Feedback Tuningfuzzy controlrobust stability

In this paper, we obtain the reduced order model for the linear discrete-time control systems using the dominant state of the control systems. Using the reduced order model, we derive necessary and sufficient conditions for the observer design of linear discrete-time control systems. Our method essentially uses the model reduction of the original linear control systems.

The present paper deals with the exposition of methods for solving the Brockett problem on the stabilization of linear control systems by a nonstationary feedback. The paper consists of two parts. We consider continuous linear control systems in the first part and discrete systems in the second part. In the first part, we consider two approaches to the solution of the Brockett problem. The first approach permits one to obtain low-frequency stabilization, and the second part deals with high-frequency stabilization. Both approaches permit one to derive necessary and sufficient stabilization conditions for two-dimensional (and three-dimensional, for the first approach) linear systems with scalar inputs and outputs. In the second part, we consider an analog of the Brockett problem for discrete linear control systems. Sufficient conditions for low-frequency stabilization of linear discrete systems are obtained with the use of a piecewise constant periodic feedback with sufficiently large period. We obtain necessary and sufficient conditions for the stabilization of two-dimensional discrete systems. In the second part, we also consider the control problem for the spectrum (the pole assignment problem) of the monodromy matrix for discrete systems with a periodic feedback.

On the Equivalence Problem of Control Systems and Control Systems with Timelags in the Theory of Stabilization

This article presents the central finite-dimensional H ∞ controller for linear time-varying systems with unknown parameters, that is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, this article reduces the original H ∞ controller problem to the corresponding H 2 controller problem, using the technique proposed in Doyle et al. [Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), ‘State-space Solutions to Standard H 2 and H Infinity Control Problems’, IEEE Transactions Automatic Control, 34, 831–847]. This article yields the central suboptimal H ∞ controller for linear systems with unknown parameters in a closed finite-dimensional form, based on the corresponding H 2 controller obtained in Basin and Calderon-Alvarez [Basin, M.V., and Calderon-Alvarez, D. (2008), ‘Optimal LQG Controller for Linear Systems with Unknown Parameters’, Journal of The Franklin Institute, 345, 293–302]. Numerical simulations are conducted to verify performance of the designed central suboptimal controller for uncertain linear systems with unknown parameters against the conventional central suboptimal H ∞ controller for linear systems with exactly known parameter values.