An iterative approach for the discrete‐time dynamic control of Markov jump linear systems with partial information

The , and mixed dynamic output feedback control of Markov jump linear systems in a partial observation context is studied through an iterative approach. By partial information, we mean that neither the state variable x(k) nor the Markov chain θ(k) are available to the controller. Instead, we assume that the controller relies only on an output y(k) and a measured variable coming from a detector that provides the only information of the Markov chain θ(k). To solve the problem, we resort to an iterative method that starts with a state‐feedback controller and solves at each iteration a linear matrix inequality optimization problem. It is shown that this iterative algorithm yields to a nonincreasing sequence of upper bound costs so that it converges to a minimum value. The effectiveness of the iterative procedure is illustrated by means of two examples in which the conservatism between the upper bounds and actual costs is significantly reduced.     

Switching controller design for linear time invariant plant with a single I/O delay

ABSTRACT

To deal with the problem of conflicting requirements that cannot be satisfied by only a single LTI controller, this paper focuses on the design of a switching controller, which includes several stabilising linear time-invariant (LTI) controllers designed independently with different control performance criteria, for a specific LTI plant with a single I/O delay. The switching controller design procedure is divided into three steps. First, using simple loop shifting arguments, the design problem is reducible to an equivalent delay-free one. Second, traditional LTI controller synthesis methods could be considered independently for the delay-free plant. Third, based on a quadratically stable state space realisation method, a Youla parameter including a switching strategy with these controllers is designed to guarantee different requirements. Finally, a numerical example is provided to demonstrate the validity and efficiency of the approach.     

On the tuning of predictive controllers: Impact of disturbances,constraints, and feedback structure

The impact of problem formulation modifications on predictive controller tuning is investigated. First, the proposed tuning method is shown to adapt to disturbance characteristic changes and thus, takes full economic advantage of the scenario. The second topic concerns point‐wise‐in‐time constraints and the impact of constraint infeasibility. Specifically, we shift the tuning question from selection of nonintuitive weighting matrix parameters to that of a few key parameters and results in a rather intuitive trade‐off between expected profit and expected constraint violations. Finally, we show that simple modifications will allow for the consideration of various feedback structures, including computational delay and partial state information. The overall conclusions of the work are that the results of the automated algorithm will help build an intuitive understating of the dynamics of the process and ultimately result in a higher level trade‐off between profit and constraint observance. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3473–3489, 2014     

Multiple integral inequalities and stability analysis of time delay systems

This paper is devoted to stability analysis of continuous-time delay systems based on a set of Lyapunov–Krasovskii functionals. New multiple integral inequalities are derived that involve the famous Jensen’s and Wirtinger’s inequalities, as well as the recently presented Bessel–Legendre inequalities of Seuret and Gouaisbaut (2015) and the Wirtinger-based multiple-integral inequalities of Park et al. (2015) and Lee et al. (2015). The present paper aims at showing that the proposed set of sufficient stability conditions can be arranged into a bidirectional hierarchy of LMIs establishing a rigorous theoretical basis for comparison of conservatism of the investigated methods. Numerical examples illustrate the efficiency of the method.     

Discretization and event triggered digital output feedback control of LPV systems

This paper investigates the problem of discretization and digital output feedback control design for continuous-time linear parameter-varying (LPV) systems subject to a time-varying networked-induced delay. The proposed discretization procedure converts a continuous-time LPV system into an equivalent discrete-time LPV system based on an extension of the Taylor series expansion and using an event-based sampling. The scheduling parameters are continuously measured and modeled as piecewise constant. A new transmission of the measured output to the controller is triggered by significant changes in the parameters, yielding time-varying transmission intervals. The obtained discretized model has matrices with polynomial dependence on the time-varying parameters and an additive norm-bounded term representing the discretization residual error. A two step strategy based on linear matrix inequality conditions is then proposed to synthesize a digital static scheduled output feedback control law that stabilizes both the discretized and the LPV model. The conditions can also be used to provide robust (i.e., independent of the scheduling parameter) static output feedback controllers. The viability of the proposed design method is illustrated through numerical examples.     

Extended dissipativity-based non-fragile control for multi-area power systems with actuator fault

This paper addresses the issue of reliable load frequency control design of an uncertain multi-area power system with constant time delays and disturbances via non-fragile sampled-data control approach. In particular, the parameter uncertainties are assumed to be randomly occurring which are described by the Bernoulli distributed sequences. By constructing a suitable Lyapunov–Krasovskii functional together with Wirtinger-based inequality, a new set of sufficient conditions in terms of linear matrix inequalities is obtained to ensure the asymptotic stability and extended dissipativity of the multi-area power system not only when all actuators are operational, but also in case of some actuator failures. Finally, simulation results are conducted to validate the effectiveness of the proposed control design technique.     

Complete convergence of stochastic approximation algorithm in ℝd under random noises

In this article, we study a stochastic approximation algorithm that approximates the exact root θ of a function M defined in ?^d into ?^d. The function M cannot be known exactly, but only noisy measurements are available at each point x_n with the error ξ_n. The sequence of noise (_ξn)n is random; we treat both cases where it is independent and dependent and we establish the complete convergence of the approximated sequence of θ.