Guoyong Shi

On the input-to-state stability (ISS) of a double integrator with saturated linear control laws

We show that the closed loop system consisting of a double integrator with any stabilizing saturated linear control law is not input-to-state stable (ISS) even for external disturbances with arbitrarily small magnitude.

On L/sub p/ (l/sub p/) performance with global internal stability for linear systems with actuators subject to amplitude and rate saturations

It has been shown that for critically unstable systems with saturating actuators one can not simultaneously achieve the global internal stabilization and the global finite-gain L/sub p/ (l/sub p/) performance whenever the external input (disturbance) is not input-additive. However, one can achieve the global internal stabilization and global L/sub p/ (l/sub p/) stabilization (without finite-gain) for any p/spl isin/[1,/spl infin/). In this paper we show that for null controllable systems with actuators subject to amplitude and rate saturations, the L/sub p/ (l/sub p/) performance (without finite gain) with global internal stability can be achieved.

On optimal output regulation for linear systems

The classical output regulation problem formulation for linear systems has a number of shortcomings; among them a primary one is that it does not take into account the transient response. Although this problem has been studied since the 1970s, a complete picture has not emerged yet. We formulate and study here a number of output regulation problems which incorporate the notion of transient performance into them. By defining a performance index that involves transient response, we define optimal and suboptimal control problems which are constrained by the steady state output regulation requirement. Such constrained optimal and suboptimal control problems for a given system are studied by transforming them to unconstrained optimal and suboptimal control problems for certain auxiliary systems. Several issues such as obtaining expressions for the infimal performance measure, solvability conditions, regulator construction are studied in detail. Both state and measurement feedback controllers are considered.

Semi-global stabilization and output regulation of constrained linear plants via measurement feedback

Semi-global stabilization and output regulation of linear systems subject to state and/or input constraints have been studied in our earlier work by using state feedback. For the same problems, observer based measurement feedback control designs are the topics of this paper. High-gain observers are used in the feedback design in order to obtain accurate estimates of the state so that the constraint violation can be avoided. Due to the peaking phenomenon associated with a high-gain observer, a special saturation protection is built in the control laws to avoid possible constraint violation. The results in this paper show that the semi-global stabilization and semi-global output regulation problems for constrained linear systems are solvable via measurement feedback under solvability conditions similar to those in the state feedback.

On achieving L/sub p/ (l/sub p/) performance with global internal stability for linear plants with saturating actuators

We show that for both continuous-time and discrete-time critically unstable linear systems with saturating actuators one can not simultaneously achieve the global internal stabilization and the global finite-gain L/sub p/ (l/sub p/) performance whenever the external input (disturbance) is not input-additive. However, one can achieve the global internal stabilization and global L/sub p/ (l/sub p/) stabilization (without finite-gain) for any p/spl isin/[1:/spl infin/).

Output regulation of linear plants subject to constraints

Output regulation problems for continuous-time linear systems with state and/or input constraints are studied. The problems are formulated in global and semi-global setting by using state or full information feedback. The goal of this paper is to develop solvability conditions for the posed problems. Moreover, appropriate regulators are constructed under the solvability conditions. To state the solvability conditions clearly, a taxonomy of constraints is introduced which delineates the constraints into several categories. Such a taxonomy of constraints provides a classification of linear plants with constraints and identifies what types of output regulation problems are solvable. Results developed here include as a special case the results obtained in the literature for systems with only input constraints. The constraint taxonomy also identifies some intrinsically hard constraints (non-right invertible constraints) for which the solvability conditions of global/semi-global output regulation problems are not clear yet. As a special case of output regulation, we also consider tracking problems with constraints. It is shown that if there exists a state feedback controller with a stabilizing domain of attraction, then one can find a regulator with a tracking domain of attraction arbitrarily close to the stabilizing domain.

Internal stabilization and external L/sub P/ stabilization of linear systems subject to constraints

Having studied during the last decade several aspects of several control design problems for linear systems subject to magnitude and rate constraints on control variables, during the last two years the research has broadened to include magnitude constraints on control variables as well as state variables. Recent work by Han et al. (2000), Hou et al. (1998) and Saberi et al. (2002) considered linear systems in a general framework for constraints including both input magnitude constraints as well as state magnitude constraints. In particular, Saberi et al. consider internal stabilization while Han et al. consider output regulation in different frameworks, namely a global, semiglobal, and regional framework. These problems require very strong solvability conditions. Therefore, a main focus for future research should focus on finding a controller with a large domain of attraction and some good rejection properties for disturbances restricted to some bounded set.

On optimal output regulation for linear systems-state feedback

In this paper we revisit the classical output regulation problem for linear systems, and generalize the problem formulation in order to incorporate the notion of transient performance into it. Both optimal and suboptimal output regulation via state feedback are considered. Issues such as expression for the infimal performance measure, solvability conditions, regulator constructions and structural properties of the optimal performance are studied in detail.

Generalized output regulation of linear plants with actuators subject to amplitude and rate saturations

We revisit the so called generalized output regulation problem for linear systems with input subject to both amplitude and rate saturations. We consider the generalized regulation problems via state and measurement feedback for both continuous-time and discrete-time systems. The underlying design philosophy is that the actuator constraints are modeled as an operator and are incorporated in the controller so that the control signals do not overload the actuators.