Relay control of systems with parameter uncertainties and disturbances

This paper presents an approach, using a semidefinite Liapunov function, for designing a model-tracking system with a relay controller. The effect of parameter uncertainties and disturbance inputs is considered. It is shown that, by this method, the state variables need not be in phase variable form, as has been formerly required. This results in a reduction of instrumentation noise entering the system, and a more reasonable solution to the problem of disturbance rejection. Application of the method is made to the control of an unstable system. Specifically, experimental data on control of a cart-supported inverted pendulum is presented.     

Stability analysis and gain-scheduled state feedback control for continuous-time systems with bounded parameter variations

The problems of robust stability analysis and state feedback control based on gain-scheduling for continuous-time systems with time-varying parameters that have bounded rates of variation and lie inside a polytope are addressed in this article. With respect to previous results in the literature, two main contributions of the article are: (i) the robust stability analysis conditions are less conservative and demand less computational effort than the existing ones; (ii) the conditions can be extended to cope with the problem of control design for this class of system. Parameter-dependent linear matrix inequality (LMI) conditions are given for the existence of a parameter-dependent Lyapunov function quadratic in the state and homogeneous polynomially of arbitrary degree in the parameter assuring robust stability. Two convex procedures based on LMIs exhibiting distinct complexities are proposed to solve the problem of robust stability. An extension to deal with the computation of a stabilising parameter-dependent state feedback gain for this class of time-varying systems is also provided, as a sequence of LMIs of increasing precision. Examples illustrate the results, including comparisons with other techniques from the literature.     

Linear quadratic regulation of systems with stochastic parameter uncertainties

In this paper, we develop a theoretical framework for linear quadratic regulator design for linear systems with probabilistic uncertainty in the parameters. The framework is built on the generalized polynomial chaos theory. In this framework, the stochastic dynamics is transformed into deterministic dynamics in higher dimensional state space, and the controller is designed in the expanded state space. The proposed design framework results in a family of controllers, parameterized by the associated random variables. The theoretical results are applied to a controller design problem based on stochastic linear, longitudinal F16 model. The performance of the stochastic design shows excellent consistency, in a statistical sense, with the results obtained from Monte-Carlo based designs.     

Adaptive control for systems with bounded disturbances

The authors present an identification algorithm that can be used to design globally stable indirect adaptive controllers for minimum- and nonminimum-phase systems subject to bounded disturbances. The parameter estimation scheme is a least-squares algorithm with dead zone. The dead zone is such that the estimates converge and make it possible to define projected estimates having the same convergence properties as the original estimates. In the minimum-phase case, the projection facility can be used to ensure that the leading coefficient projected estimate is greater than or equal to the true leading coefficient in absolute value. The projection procedure can also be used to avoid pole-zero cancellations in an adaptive pole-placement algorithm     

On the stability of receding horizon control for continuous-time stochastic systems

We study the stability of receding horizon control for continuous-time non-linear stochastic differential equations. We illustrate the results with a simulation example in which we employ receding horizon control to design an investment strategy to repay a debt.     

Guaranteed cost control of systems with norm bounded uncertainties

Feedback controller design based on an imprecisely known plant model may cause performance degradation and even instability of the closed-loop system. It is therefore important to design robust controllers using a priori information on the model uncertainties. The method presented in this paper considers uncertainties satisfying bounding constraints, and ensures closed-loop stability as well as satisfactory performances characterized by a quadratic cost functional that remains bounded in the presence of uncertainties of the above class.     

Distributed stochastic MPC for systems with parameter uncertainty and disturbances

A distributed stochastic model predictive control algorithm is proposed for multiple linear subsystems with both parameter uncertainty and stochastic disturbances, which are coupled via probabilistic constraints. To handle the probabilistic constraints, the system dynamics is first decomposed into a nominal part and an uncertain part. The uncertain part is further divided into 2 parts: the first one is constrained to lie in probabilistic tubes that are calculated offline through the use of the probabilistic information on disturbances, whereas the second one is constrained to lie in polytopic tubes whose volumes are optimized online and whose facets' orientations are determined offline. By permitting a single subsystem to optimize at each time step, the probabilistic constraints are then reduced into a set of linear deterministic constraints, and the online optimization problem is transformed into a convex optimization problem that can be performed efficiently. Furthermore, compared to a centralized control scheme, the distributed stochastic model predictive control algorithm only requires message transmissions when a subsystem is optimized, thereby offering greater flexibility in communication. By designing a tailored invariant terminal set for each subsystem, the proposed algorithm can achieve recursive feasibility, which, in turn, ensures closed‐loop stability of the entire system. A numerical example is given to illustrate the efficacy of the algorithm.     

Ensemble control of linear systems with parameter uncertainties

In this paper, we study the optimal control problem for a class of four-dimensional linear systems based on quaternionic and Fourier analysis. When the control is unconstrained, the optimal ensemble controller for this linear ensemble control systems is given in terms of prolate spheroidal wave functions. For the constrained convex optimisation problem of such systems, the quadratic programming is presented to obtain the optimal control laws. Simulations are given to verity the effectiveness of the proposed theory.     

Adaptive control of continuous-time linear stochastic systems

An adaptive control problem for linear, continuous-time stochastic systems is described and solved in this paper. A solution of the adaptive control problem means that the family of maximum likelihood estimators is shown to be strongly consistent and the average costs are shown to converge to the optimal average costs. The unknown parameters in the model appear affinely in the drift term of the stochastic differential equation. The assumptions that are made for the solution are natural and verifiable. A recursive equation is given for the maximum likelihood estimates. This research was partially supported by NSF Grants ECS-8403286-A01 and ECS-8718026.     

Linearization and optimization of stochastic systems with bounded control

An approach using statistical linearization to an optimization problem for stochastic systems with bounded control is presented. The cost functional to be minimized is the stationary expectation of a quadratic function of the state and control variables. The class of control laws to be considered is a nonlinear function (saturation or bang-bang) of a linear combination of the state variables. Via linearization, the problem is then reduced to a parameter optimization problem. For the class of saturation functions, a property of the linearized gain is used to establish the unique minimum of the cost functional. The solution for the class of the bang-bang control functions is obtained by a technique using a Lagrange multiplier.     

Leader-following consensus of nonlinear multi-agent systems with randomly occurring uncertainties and stochastic disturbances under impulsive control input

This paper focuses on the leader-following consensus problem of nonlinear multi-agent systems with randomly occurring uncertainties and stochastic disturbances under impulsive control input. Based on the average impulsive interval, a unified consensus criterion is derived for multi-agent systems. On the other hand, our consensus criterion is applicable to impulsive control sequences in which the lower bound of impulsive interval is allowed to be arbitrarily small and the upper bound of impulsive interval is allowed to be big enough. The proposed consensus criterion is theoretically and numerically proved to be less conservative than existing results. Two numerical simulations illustrate the effectiveness of theoretical results.     

Exponential stability of switched stochastic delay systems with non-linear uncertainties

This article considers the robust exponential stability of uncertain switched stochastic systems with time-delay. Both almost sure (sample) stability and stability in mean square are investigated. Based on Lyapunov functional methods and linear matrix inequality techniques, new criteria for exponential robust stability of switched stochastic delay systems with non-linear uncertainties are derived in terms of linear matrix inequalities and average dwell-time conditions. Numerical examples are also given to illustrate the results.     

Sampled-data-based LQ control of stochastic linear continuous-time systems

Sampled-data (SD) based linear quadratic (LQ) control problem of stochastic linear continuous-time (LCT) systems is discussed. Two types of systems are involved. One is time-invariant and the other is time-varying. In addition to stability analysis of the closed-loop systems, the index difference between SD-based LQ control and conventional LQ control is investigated. It is shown that when sample time ?T is small, so is the index difference. In addition, the upper bounds of the differences are also presented, which are O(?T2) and O(?T), respectively.     

Robust stability of multivariable systems with both real parametricand norm bounded uncertainties

The robust stability of a multivariable system with both structured real parametric and unstructured norm bounded uncertainties is considered. It is shown that if the real parametric uncertainty enters only linearly and independently into the numerator matrix and the denominator characteristic polynomial, then the robust stability (or stability margin) can be tested (or calculated) exactly. It is also shown that this in fact gives a way to compute a class of real structured singular values     

Adaptive robust control of nonholonomic systems with stochastic disturbances

Based on the Brockett’s necessary condition for feedback asymptotic stabilization[1], nonholonomic systems fail to be stabilized at the origin by any static continuous state feedback though they are open loop controllable. There are two novel approaches …     

Distributed robust control of linear multi-agent systems with parameter uncertainties

This article considers the distributed robust control problems of uncertain linear multi-agent systems with undirected communication topologies. It is assumed that the agents have identical nominal dynamics while subject to different norm-bounded parameter uncertainties, leading to weakly heterogeneous multi-agent systems. Distributed controllers are designed for both continuous- and discrete-time multi-agent systems, based on the relative states of neighbouring agents and a subset of absolute states of the agents. It is shown for both the continuous- and discrete-time cases that the distributed robust control problems under such controllers in the sense of quadratic stability are equivalent to the H _∞ control problems of a set of decoupled linear systems having the same dimensions as a single agent. A two-step algorithm is presented to construct the distributed controller for the continuous-time case, which does not involve any conservatism and meanwhile decouples the feedback gain design from the communication topology. Furthermore, a sufficient existence condition in terms of linear matrix inequalities is derived for the distributed discrete-time controller. Finally, the distributed robust H _∞ control problems of uncertain linear multi-agent systems subject to external disturbances are discussed.     

BMI-based stability and performance design for fuzzy-model-based control systems subject to parameter uncertainties.

This paper presents the stability and performance design of a fuzzy-model-based control system subject to parameter uncertainties. A nonlinear controller with a favorable characteristic to relax the stability conditions is proposed to drive the system states of the nonlinear plant to follow those of a stable reference model. Stability and performance conditions in terms of bilinear matrix inequalities (BMIs) will be derived based on a Lyapunov-based approach. A combined genetic algorithm and convex programming technique process will be developed to solve the solution to the BMIs. An application example will be given to illustrate the merits of the proposed approach.     

参数不确定离散混沌系统的模糊脉冲控制

研究了参数不确定离散混沌系统的控制问题.通过Takagi-Sugeno(TS)模糊动态模型和脉冲控制技术,建立了参数不确定离散混沌系统的Takagi-Sugeno模糊脉冲控制模型,然后利用矩阵分析和Lyapunov稳定性理论,得到了参数不确定离散混沌系统控制的一个充分条件,最后通过实例证实了该结果的正确性,相比传统的控制方法,基于Takagi-Sugeno模型的模糊脉冲控制方法具有一定的优越性.