Constrained discrete-time PI controller design for output PDFs of stochastic systems with time delays

This article presents a new proportional-integral (PI) tracking control strategy for non-Gaussian stochastic systems based on a square root B-spline model for the output probability density functions (PDFs). Following the square root B-spline approximation to the measured output PDF, a non-linear discrete-time dynamical model can be established between the control input and the weights related to the PDFs. It is noted that the PDF tracking is transformed to a constrained dynamical tracking control problem for weight dynamics. For the non-linear discrete-time weight model including time-delay terms and exogenous disturbances, convex linear matrix inequality optimisation algorithms are used to design a generalised PI controller such that stabilisation, state constraint and tracking performance can be guaranteed simultaneously. Furthermore, in order to enhance the robustness, the peak-to-peak measure index is applied to optimise the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.     

Discrete-time output feedback sliding-mode control design for uncertain systems using linear matrix inequalities

An output feedback-based sliding-mode control design methodology for discrete-time systems is considered in this article. In previous work, it has been shown that by identifying a minimal set of current and past outputs, an augmented system can be obtained which permits the design of a sliding surface based upon output information only, if the invariant zeros of this augmented system are stable. In this work, a procedure for realising discrete-time controllers via a particular set of extended outputs is presented for non-square systems with uncertainties. This method is applicable when unstable invariant zeros are present in the original system. The conditions for existence of a sliding manifold guaranteeing a stable sliding motion are given. A procedure to obtain a Lyapunov matrix, which simultaneously satisfies both a Riccati inequality and a structural constraint, is used to formulate the corresponding control to solve the reachability problem. A numerical method using linear matrix inequalities is suggested to obtain the Lyapunov matrix. Finally, the design approach given in this article is applied to an aircraft problem and the use of the method as a reconfigurable control strategy in the presence of sensor failure is demonstrated.     

Fault detection and diagnosis for delay-range-dependent stochastic systems using output PDFs

International Journal of Control, Automation and Systems - This paper investigates a new fault detection and diagnosis(FDD) scheme for delay-range-dependent stochastic systems. Compared with...     

An improved output feedback controller design for linear discrete-time systems using a matrix decomposition method

This paper presents the design of output feedback controllers for discrete-time (DT) linear systems. New sufficient LMI conditions are derived for designing static $H_2$ and $H_{\infty }$ controllers using decomposition of an auxiliary matrix. The decomposition facilitates linearization of nonlinear term of reduced size to obtain linear matrix inequality criteria. This leads to less conservative results as shown in the numerical examples. In addition, the proposed static output feedback criteria is also used for designing dynamic output feedback controllers for DT systems. Furthermore, a comparative study is also made for the proposed design method with the results existing in the literature. Finally, a DT static output feedback $H_{\infty }$ controller is designed for a quarter-car suspension system. Simulation results are provided to show the efficacy of the proposed design method.     

Observer design for wired linear networked control systems using matrix inequalities

We design an observer-protocol pair to asymptotically reconstruct the states of a linear time-invariant (LTI) plant under communication constraints induced by the network. We parameterize a class of observers and protocols, and for a given network transmission interval, we derive sufficient conditions in terms of matrix inequalities for the existence of an observer-protocol pair in the considered class that asymptotically reconstructs the plant states.     

Fuzzy observer design using linear matrix inequalities for fuzzy closed-loop control systems

Linear observers play an important role in modern control theory and practice. A systematic design method of fuzzy observers would be important for fuzzy control as well. The fuzzy observer is designed by solving linear matrix inequalities (LMI) that represent control performance such as disturbance rejection and robust stability. Our approach in designing the fuzzy observer is based on the LMI formulation of the stability conditions for closed-loop Takagi-Sugeno (T-S) fuzzy systems, when states are not available for measurement of feedback. We present a new approach, which is to design an observer based on fuzzy implications, with fuzzy sets in the antecedents, and an asymptotic observer in the consequents. Each fuzzy rule is responsible for observing the states of a locally linear subsystem. An example illustrates the design procedure.     

Sliding-mode output feedback controller design using linear matrixinequalities

Considers a sliding-mode controller which requires only output information and is static in nature. The novelty of the approach is in the rationale and method used to synthesize the linear control component which involves a linear matrix inequality optimization. The so-called reachability condition used in sliding-mode controller analysis is not required to be satisfied globally. Instead, sliding is only expected to take place within a subset of the state-space referred to as the sliding patch     

具有时滞的奇异系统H∞控制

针对具有时滞的奇异系统H_∞输出反馈控制问题, 利用Lyapunov泛函方法, 得到闭环系统稳定且具有H_∞-范数界γ的充分条件, 基于相应的LMI可行解给出了动态控制器显式表示. 最后, 数值例子表明了该方法的正确性.     

Linearized controller design for the output probability density functions of non-Gaussian stochastic systems

1 Introduction There are many practical systems that require the control of the shape of the output probability den- sity function rather than just their mean values and variances. These systems are seen in papermaking processes[1,2], chemical engineering, material science, combustion ?ame distribution systems and food pro- cessing industries. For example, in chemical engineer- ing the control of particle size distribution has al- ways been regarded as an important area of research[3], whilst …     

具有时滞的奇异系统H∞控制

针对具有时滞的奇异系统H∞输出反馈控制问题,利用Lyapunov泛函方法,得到闭环系统稳定且具有H∞-范数界γ的充分条件,基于相应的LMI可行解给出了动态控制器显式表示.最后,数值例子表明了该方法的正确性.     

Robust output feedback model predictive control using off-line linear matrix inequalities

A fundamental question about model predictive control (MPC) is its robustness to model uncertainty. In this paper, we present a robust constrained output feedback MPC algorithm that can stabilize plants with both polytopic uncertainty and norm-bound uncertainty. The design procedure involves off-line design of a robust constrained state feedback MPC law and a state estimator using linear matrix inequalities (LMIs). Since we employ an off-line approach for the controller design which gives a sequence of explicit control laws, we are able to analyze the robust stabilizability of the combined control laws and estimator, and by adjusting the design parameters, guarantee robust stability of the closed-loop system in the presence of constraints. The algorithm is illustrated with two examples.     

Exponential dynamic output feedback controller design for stochastic neutral systems with distributed delays

This paper investigates the problem of stochastic stabilization for stochastic neutral systems with distributed delays. The time delay is assumed to appear in both the state and measurement equations. Attention is focused on the design of linear dynamic output feedback controllers such that the resulting closed-loop system is exponentially mean-square stable. A sufficient condition for the solvability of the problem is obtained in terms of a linear matrix inequality (LMI). When this LMI is feasible, an explicit expression of a desired dynamic output feedback controller is also given. The theory developed in this paper is demonstrated via a numerical example.     

Constrained PID tracking control for output PDFs of non‐gaussian stochastic system based on LMIs

This paper presents a new PID tracking control strategy for general non‐Gaussian stochastic systems based on a square root B‐spline model for the output probability density functions (PDFs). Using the B‐spline expansion with modeling errors and the nonlinear weight model with exogenous disturbances, the PDF tracking is transformed to a constrained dynamical tracking control problem for weight vectors. Instead of the non‐convex design algorithms, the generalized PID controller structure and the improved convex linear matrix inequality (LMI) algorithms are proposed to fulfil the PDF tracking problem. Meanwhile, in order to enhance robustness, the robust peak‐to‐peak measure is applied to optimize the tracking performance. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A stochastic PID controller for a class of MIMO systems

This paper deals with the design of a controller possessing tracking capability of any realisable reference trajectory while rejecting measurement noise. We consider discrete-time-varying multi-input multi-output stable linear systems and a proportional-integral-derivative (PID) controller. A novel recursive algorithm estimating the time-varying PID gains is proposed. The development of the proposed algorithm is based on minimising a stochastic performance index. The implementation of the proposed algorithm is described and boundedness of trajectories and convergence characteristics are presented for a discretised continuous-time model. Simulation results are included to illustrate the performance capabilities of the proposed algorithm.     

Robust PID controller design for processes with stochastic parametric uncertainties

The stability and performance of a system can be inferred from the evolution of statistical characteristics of the system's states. Wiener's polynomial chaos can provide an efficient framework for the statistical analysis of dynamical systems, computationally far superior to Monte Carlo simulations. This work proposes a new method of robust PID controller design based on polynomial chaos for processes with stochastic parametric uncertainties. The proposed method can greatly reduce computation time and can also efficiently handle both nominal and robust performance against stochastic uncertainties by solving a simple optimization problem. Simulation comparison with other methods demonstrated the effectiveness of the proposed design method.     

Simultaneous controller design for linear time-invariant systems

The use of generalized sampled-data hold functions (GSHF) in the problem of simultaneous controller design for linear time-invariant plants is discussed. This problem can be stated as follows: given plants P₁, P₂, . . ., P_N , find a controller C which achieves not only simultaneous stability, but also simultaneous optimal performance in the N given systems. By this, it is meant that C must optimize an overall cost function reflecting the closed-loop performance of each plant when it is regulated by C. The problem is solved in three aspects: simultaneous stabilization, simultaneous optimal quadratic performance, and simultaneous pole assignment in combination with simultaneous intersampling performance     

Dynamic output feedback controller design for fuzzy systems

This paper presents dynamic output feedback controller design for fuzzy dynamic systems. Three kinds of controller design methods are proposed based on a smooth Lyapunov function or a piecewise smooth Lyapunov function. The controller design involves solving a set of linear matrix inequalities (LMI's) and the control laws are numerically tractable via LMI techniques. The global stability of the closed-loop fuzzy control system is also established.     

Simultaneous controller design for time-varying linear systems

In this paper, we establish the parametrization of all simultaneously stabilizing controllers for two time-varying linear systems. A new approach to the simultaneous stabilization of three time-varying linear systems is also provided.     

Sensor fault diagnostics for a class of non-linear systems using linear matrix inequalities

This paper develops a systematic approach to fault diagnostic system design for sensor health monitoring in Lipschitz non-linear systems. The methodology applies to non-linear systems with three or more sensors in which the state is observable through any one of the sensor measurements. Two major issues are addressed in the paper—observer design for the non-linear system to ensure directional growth of residues for failure identification and use of linear matrix inequalities for explicit design of the observer gain. The use of the methodology is demonstrated through an illustrative example.