Generalized $${{\mathcal{H}}}_{2}$$ H 2 Control of a Linear Continuous-Discrete System on a Finite Horizon
- PDF / 464,082 Bytes
- 11 Pages / 612 x 792 pts (letter) Page_size
- 92 Downloads / 146 Views
PICAL ISSUE
Generalized H2 Control of a Linear Continuous-Discrete System on a Finite Horizon R. S. Biryukov Nizhny Novgorod State University of Architecture and Civil Engineering, Nizhny Novgorod, Russia e-mail: [email protected] Received July 23, 2019 Revised October 5, 2019 Accepted January 30, 2020
Abstract—This paper considers a linear continuous-discrete time-varying system described by a set of differential and difference equations on a finite horizon. For such a hybrid system, the concept of the generalized H2 norm is introduced, representing the induced norm of a linear operator generated by the system under consideration. This norm is characterized in terms of Lyapunov difference equations and also in terms of recursive linear matrix inequalities. Discrete time-varying optimal controllers, including multiobjective ones, that minimize the generalized H2 norm of the closed loop system are designed. Keywords: linear time-varying hybrid system, generalized H2 norm, optimal control, multiobjective optimization DOI: 10.1134/S0005117920080032
1. INTRODUCTION As a rule, modern control systems are implemented in digital form, whereas real objects operate in continuous time. Due to such a separation, a controller uses the values of a continuous signal coming from an object only at discrete time instants. For this reason, it is important to design a discrete-time controller that will consider the behavior of an object at time instants between successive measurements, as much as possible. One of the performance criteria for assessing a control system is the maximum deviation of its target output from some nominal value with respect to an external disturbance. The concept of the generalized H2 norm as the maximum ratio of the time-maximal value of the Euclidean output norm to the L2 norm of an uncertain external disturbance was introduced in [10] for the class of continuous-time systems and in [5] for the class of discrete-time ones. The existence conditions of an optimal output controller on infinite horizon, in terms of Riccati equations and in terms of linear matrix inequalities (LMIs), were established in [1, 9, 11]. The concept of the maximum deviation as a natural extension of the generalized H2 norm to the class of systems with a nonzero initial state was suggested in [2–4], in the cases of continuous and discrete time. For continuous-discrete systems described by a set of differential and difference equations on infinite horizon, some estimates of the generalized H2 norm were derived in [6–8]. In addition, controllers minimizing the upper bound of the norm were designed, in terms of linear matrix inequalities [7, 8] and in terms of the Riccati differential equations [6]. This paper deals with a continuously-discrete time-varying system with a discrete target output and nonzero initial conditions on a finite horizon. Following the research works [2–4, 10], the 1394
GENERALIZED H2 CONTROL
1395
concept of the generalized H2 norm is introduced, representing the induced norm of a linear operator generated by the syst
Data Loading...
