Piecewise State Feedback Controller Research Articles

Fuzzy model-based controller synthesis for networked nonlinear systems with event triggering communication scheme

ABSTRACTIn this paper, the problem of event-triggered piecewise controller design is concerned for discrete-time networked nonlinear systems represented by T–S fuzzy models. Based on the event triggering communication strategy, only the state information of the plant that violates a predefined triggering condition is transmitted in the shared communication channels. Considering that the premise variables of the plant in the form of T–S fuzzy representation are not synchronously available at the controller side, a novel approach to the piecewise state feedback controller design is proposed via some matrix inequality convexification techniques such that the closed-loop T–S fuzzy system is asymptotically stable with a guaranteed performance level. By introducing the Jensen inequality method, some cross products of two vectors are eliminated, which greatly facilitates the controller design procedure. Finally, some illustrative examples are provided to illustrate the effectiveness of the proposed method.

Observer‐based output feedback compensator design for linear parabolic PDEs with local piecewise control and pointwise observation in space

This study presents an observer-based output feedback compensator design for a linear parabolic partial differential equation (PDE), where a finite number of actuators and sensors are active over partial areas and at specified points in the spatial domain, respectively. In the proposed design method, a Luenberger-type PDE observer is first constructed by using the non-collocated pointwise observation to exponentially track the PDE state. Based on the estimated state, a collocated local piecewise state feedback controller is then proposed. By employing a Lyapunov direct method, integration by parts, Wirtinger's inequality and first mean value theorem for definite integrals, sufficient conditions on the exponential stability of the resulting closed-loop coupled PDEs are presented in terms of standard linear matrix inequalities. Furthermore, both open-loop and closed-loop well-posedness analysis results are also established by the C 0 -semigroup method. Numerical simulation results are presented to show the effectiveness of the proposed design method.

A switched dynamical system approach towards the optimal control of chemical processes based on a gradient-based parallel optimization algorithm

This paper considers an optimal control problem of chemical processes with a novel piecewise state-feedback controller. Firstly, the chemical process optimal control problem is formulated as a switched dynamical system optimal control problem, which can be transformed into a parameter optimization problem. Next, to achieve rapid convergence from remote starting points, we propose a novel gradient-based optimization algorithm, which is suitable to a parallel implementation because the step is improved by updating its direction as well as its length simultaneously before moving to the next iteration, and the step computation involves only the inner products of vectors. Then, the convergent properties of the parameter optimization problem to the original optimal control problem are discussed. Finally, the numerical simulation results show that the gradient-based parallel optimization algorithm is an effective alternative method for solving the chemical process optimal control problems.

Observer‐based dynamic local piecewise control of a linear parabolic PDE using non‐collocated local piecewise observation

This paper employs the observer-based output feedback control technique to study the problem of local piecewise control for a linear parabolic partial differential equation(PDE) using non-collocated local piecewise observation. By the noncollocated local piecewise observation, a Luenberger-type PDE observer is first constructed to exponentially track the state of the PDE in the sense of both ℒ 2 norm and ℋ 1 norm. Based on the estimated state, a collocated local piecewise state feedback controller is then proposed for exponential stabilisation of the PDE. Sufficient conditions on exponential stabilisation of the PDE by the suggested feedback controller in the sense of both ℒ 2 norm and ℋ 1 norm are developed by utilising Lyapunov direct method, integration by parts, Wirtinger's inequality, and first mean value theorem for definite integrals, and presented in terms of standard linear matrix inequalities. The well-posedness is also analysed for both open-loop and resulting closed-loop PDE by using C 0 -semigroup approach. Finally, numerical simulation results are presented to show the effectiveness of the proposed design method.

A novel dropout compensation scheme for control of networked T–S fuzzy dynamic systems

This paper considers the problem of H∞ state feedback control for networked nonlinear systems under unreliable communication links with packet dropouts. The nonlinear plant in this paper is described by a Takagi–Sugeno (T–S) fuzzy model. The packet dropouts in both sensor-to-controller (S/C) and controller-to-actuator (C/A) channels are considered, which are modeled by Bernoulli processes. A new compensation scheme for the estimation of missing packets is proposed, and a piecewise state feedback controller is designed so that the resulting closed-loop control system is stochastically stable with guaranteed H∞ performance. Then the results are extended to the case when both network-induced delays and packet dropouts exist in communication links. Finally, some numerical examples are given to illustrate the procedure of the proposed approaches and the optimal H∞ performance in comparison to the existing approaches.

Optimal piecewise state feedback control for impulsive switched systems

In this paper, we consider a class of the optimal state feedback control problems involving switched systems with state jumps. The planning time horizon is subdivided into N subintervals, where the breakpoints are called the re-setting times. One system is used during each subinterval with a piecewise state feedback control form. The re-setting time, the feedback gain matrices and the heights of the state jumps at the re-setting times are considered as decision variables. It is shown, through a time scaling transform, that this class of optimal control problems is equivalent to an optimal parameter selection problem, where the varying re-setting time points are mapped into fixed time points. The gradient formula of the transformed cost function is derived. With this gradient formula, the optimal parameter selection problem can be solved as a nonlinear optimization problem, and the optimal control software MISER 3.3 can be used. Two illustrative examples are solved using the proposed method.