Y. William Wang

H 2 -suboptimal stable stabilization

Abstract In this paper we present two approaches for designing H 2 -suboptimal stable controllers. Both full-order and reduced-order controllers are considered.

Dissipative H2/H∞Controller Synthesis

In certain applications, such as the colocated control of flexible structures, the plant is known to be positive real. Hence, closed-loop stability is unconditionally guaranteed as long as the controller is also positive real. One approach to designing positive real controllers is the LQG-based positive real synthesis technique of Lozano-Leal and Joshi. The contribution of this paper is the extension of this positive real synthesis technique to include an H∞-norm constraint on closed-loop performanceIn certain applications, such as the colocated control of flexible structures, the plant is known to be positive real. Hence, closed-loop stability is unconditionally guaranteed as long as the controller is also positive real. One approach to designing positive real controllers is the LQG-based positive real synthesis technique of Lozano-Leal and Joshi. The contribution of this paper is the extension of this positive real synthesis technique to include an H/sub /spl infin//-norm constraint on closed-loop performance. >

Dissipative H2/H¿ controller synthesis

In certain applications, such as the control of flexible structures, the plant transfer function is known to be psitive real. This property arises if the sensor and actuator are colocated and also dual, for example, force actuator and velocity sensor or torque actuator and angular rate sensor. In practice, the prospects for controlling such systems is quite good since, if sensor and actuator dynamics are negligible, stability is unconditionally guaranteed so long as the controller is strictly positive real [1-3]. Although there is no general theory yet available for designing positive real controllers, a variety of techniques have been proposed based on H2 theory [4-10] and H∞, theory [11,12]. In this paper we focus on the H2-based positive real controller synthesis method of Lozano-Leal and Joshi [7]. In [7] it is shown that if the plant is positive real and if the error and disturbance matrices satisfy certain constraints, then the LQG controller is also positive real. This approach is appealing in practice since it requires only standard LQG synthesis techniques. Our goal in this note is to extend the synthesis technique of [7] to include an H∞ norm bound on the closed-loop transfer function [13]. This extension thus provides the control designer with more flexibility in specifying closed-loop system performance.

H2 optimal control with an a-shifted pole constraint

Modified Lyapunov equations for regional pole constraints in H2 synthesis have been considered in recent papers. This approach involves a constraint equation for enforcing the pole constraints and leads to an auxiliary cost that overbounds the original H2 performance. The auxiliary cost can then be used for optimization with respect to the modified Lyapunov equations that characterize the constraint region. In this paper, we consider an α-shifted constraint region and show that an augmented system whose order is twice that of the original system can be constructed to eliminate the need for an overbound so that exact H2 cost optimization can be performed. This augmented system is then utilized for closed-loop controller synthesis within a decentralized static output feedback setting. The construction of the augmented system is a refinement of the approach of Gu et al. (1992). A numerical algorithm based upon the BFGS quasi-Newton method is used for computing the optimal controller gains. The numerical resu...

L2 controller synthesis with L-bounded closed-loop impulse response

In this paper we consider an L₂ control problem with an L_∞ norm on the closed-loop impulse response. To do this we first construct an upper bound for the L_∞ norm of the closed-loop system. To perform controller synthesis, we then modify the standard LQG cost functional by including an additional penalty term that weights the L_∞ norm of the impulse response of the closed-loop system. A numerical example is given to illustrate the improved L_∞ response of the closed-loop system.