Robust Gain-Scheduling observers for continuous-time Linear Parameter-Varying systems

: Calculating the amount of information about a random function contained in another random function has important uses in communication theory. An expression for the mutual information for continuous time random processes has been given by Gelfand and Yaglom, Chiang, and Perez by generalizing Shannon's result in a natural way. Under a condition of absolute continuity of measures the continuous time expression has the same form as Shannon's result. For two Gaussian processes Gelfand and Yaglom express the mutual information in terms of a mean square estimation error. We generalize this result to diffusion processes and express the solution in a different form which is more naturally related to a corresponding filtering problem. We also use these results to calculate some information rates.

SUMMARY This paper deals with the problem of finite frequency H∞ full-order filter design for discrete-time and continuous-time linear systems, with polytopic uncertainties. Based on the generalized Kalman–Yakubovich–Popov lemma and a parameter-dependent Lyapunov function, a set of sufficient conditions are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H∞ attenuation level, from disturbance to the estimation error, is smaller than a given value over a prescribed finite frequency domain of the external disturbances. Then, in order to linearize and relax the obtained matrix inequalities, we introduce a large number of slack variables by applying Finsler's lemma twice, which provides extra degrees of freedom in optimizing the guaranteed H∞ performance. This leads to performance improvement and reduction of conservatism in the solution. It is shown later that the robust filter gains can be obtained by solving a set of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods. Copyright © 2016 John Wiley & Sons, Ltd.

In present work we consider a multidimensional linear system with additive inputs (controls) and noise governed by a Brownian motion. We allow parameters of system to change in time. In addition we assume that exact form of coefficients is not known, rather intervals within which these coefficients fluctuate are given. In addition, we do not know exact state of system, rather we observe output correlated with this state. The set of allowable controls are feedback controls based on observation of output and an ideal model dynamics. With each control we associate a performance functional characterizing the quality of tracking process and objective is to construct a robust feedback control which minimizes maximal performance functional within class of systems with nonstochastic coefficients fluctuating in same intervals as those of our problem.

This paper investigates the distributed consensus problem for linear continuous-time multi-agent systems subject to additive process noises. Due to the existence of noises, the asymptotic consensus cannot be achieved. Hence, a distributed consensus protocol is proposed such that all the agents can achieve consensus to some degree. Furthermore, based on Lyapunov theory, we characterize the consensus error under undirected and directed topologies. Numerical examples are presented to verify the effectiveness of two results.

SUMMARY The LQ+ problem, i.e. the finite-horizon linear quadratic optimal control problem with nonnegative state constraints, is studied for positive linear systems in continuous time and in discrete time. Necessary and sufficient optimality conditions are obtained by using the maximum principle. These conditions lead to a computational method for the solution of the LQ+ problem by means of a corresponding Hamiltonian system. In addition, the necessary and sufficient conditions are proved for the LQ+-optimal control to be given by the standard LQ-optimal state feedback law. Then sufficient conditions are established for the positivity of the LQ-optimal closed-loop system. In particular, such conditions are obtained for the problem of minimal energy control with penalization of the final state. Moreover, a positivity criterion for the LQ-optimal closed-loop system is derived for positive discrete-time systems with a positively invertible (dynamics) generator. The main results are illustrated by numerical examples. Copyright q 2010 John Wiley & Sons, Ltd.

This paper considers the problem of constrained stabilization of linear continuous-time systems when a quadratic cost criterion is imposed in the design of the state feedback control law. The linear quadratic regulator (LQR) is solved under positivity constraint, which means that the resulting closed-loop systems are not only optimally stable, but also positive. We focus on the class of linear continuous-time positive systems (Metzlerian systems) and use the interesting properties of Metzler matrices to provide the necessary ingredients for the main results of the paper. A two-step procedure is proposed to solve the problem. First, some necessary and sufficient conditions are presented for the existence of controllers satisfying the Metzlerian constraint, and the constrained stabilization is solved using linear programming (LP) or linear matrix inequality (LMI). Second, a sufficient condition is outlined for the existence of a solution to maintain the positivity of the first step while achieving the optimality of LQR. Finally, the robustness of the design is analyzed and possible extension of the design is proposed for an uncertain interval systems. A numerical example is included to illustrate the procedure.

Robust L∞-induced filtering and deconvolution of a wide class of linear discrete-time stochastic systems

OBSERVABILITY OF DISCRETE TIME LINEAR SWITCHING SYSTEMS1

Design of RLS-FIR filter using covariance information in linear continuous-time stochastic systems

Causal Gain-scheduled output feedback controllers using parameter-dependent Lyapunov Functions

This paper addresses the design problem of Gain-Scheduled Output-Feedback (GSOF) controllers for discretetime Linear Parameter-Varying (LPV) systems via Parameter-Dependent Lyapunov Functions (PDLFs). In our problem setting, it is supposed that scheduling parameters are provided with some uncertainties. In this practical problem setting, we give a sufficient condition for designing GSOF controllers exploiting the uncertain scheduling parameters which minimize the induced l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm in terms of Parameter-Dependent Bilinear Matrix Inequalities (PDBMIs). Two algorithms for solving the PDBMIs, i.e. line search and iterative algorithms, are shown. Under the ideal situation, i.e. exact values of scheduling parameters are available, our method then recovers the conventional design method via PDLFs.

This chapter studies null controllability of continuous-time linear systems with bounded controls. Null controllability of a system refers to the possibility of steering its state to the origin in a finite time by an appropriate choice of the admissible control input. If the system is linear and is controllable, then any state can be steered to any other location, for example, the origin, in the state space in a finite time by a control input. This implies that any controllable linear system is null controllable from any point in the state space. The control inputs that are used to drive certain states to the origin, however, might have to be large in magnitude. As a result, when the control input is limited by the actuator saturation, a linear controllable system might not be globally null controllable. In this situation, it is important to identify the set of all the states that can be steered to the origin with the bounded controls delivered by the actuators. This set is referred to as the null controllable region and is denoted as C

This article addresses the problems of robust H ∞ performance analysis and synthesis for continuous-time linear systems with time-varying uncertainties using parameter-dependent Lyapunov functions. An H ∞ performance criterion in terms of linear matrix inequalities is derived via employing a descriptor model transformation of linear systems with polytopic uncertainties (polytopic systems). This H ∞ performance criterion can be applied to robust controller synthesis and filtering design. The descriptor system approach is also taken to explore robust H ∞ performance analysis and controller synthesis of affine parameter systems. A flight control system and two numerical examples are given to illustrate the effectiveness of the proposed analysis and synthesis procedures.

A methodology for the synthesis of time-varying static output-feedback gains, capable of stabilising continuous-time linear time-varying systems, is proposed in this paper. The method is based on the computation of output-feedback gains that stabilise a family of periodic discrete-time subsystems, related to the original model, followed by a transformation that yields the desired stabilising gains for the continuous-time system. Based on such strategy, three different approaches to compute stabilising periodic discrete-time gains, as well as the necessary transformations to generate the continuous-time output-feedback gains, are proposed. Numerical examples are presented in order to compare and analyze the efficiency of the proposed approaches.

This paper is concerned with the property of asymptotic hyperstability of a continuous-time linear system under a class of continuous-time nonlinear and perhaps time-varying feedback controllers belonging to a certain class with two main characteristics; namely, (a) it satisfies discrete-type Popov’s inequality at sampling instants and (b) the control law within the intersample period is generated based on its value at sampling instants being modulated by two design weighting auxiliary functions. The closed-loop continuous-time system is proved to be asymptotically hyperstable, under some explicit conditions on such weighting functions, provided that the discrete feed-forward transfer function is strictly positive real.