Yacov Shamash

Set invariance analysis and gain-scheduling control for LPV systems subject to actuator saturation

In this paper, a set invariance analysis and gain scheduling control design approach is proposed for the polytopic linear parameter-varying systems subject to actuator saturation. A set invariance condition is first established. By utilizing this set invariance condition, the design of a time-invariant state feedback law is formulated and solved as an optimization problem with LMI constraints. A gain-scheduling controller is then designed to further improve the closed-loop performance. Numerical examples are presented to demonstrate the effectiveness of the proposed analysis and design method.

Linear controller for an inverted pendulum having restricted travel: a high-and-low gain approach

The problem of balancing an inverted pendulum has been a benchmark example in demonstrating and motivating various control design techniques. In this paper, we provide a linear state feedback design technique for balancing an inverted pendulum. The pivot of this pendulum is mounted on a carriage that has limited horizontal travel. For any given (arbitrarily small) allowable travel of the carriage, our design yields a linear state feedback controller that balances the pendulum with an infinite amount of gain margin in the sense that, if the feedback gain is perturbed by any multiplying factor greater than one, the controller will still balance the pendulum without requiring greater traveling distance than the maximum allowable.

Construction and parameterization of all static and dynamic H/sub 2/-optimal state feedback solutions, optimal fixed modes and fixed decoupling zeros

A problem of H/sub 2/ optimization via state feedback is considered. The problems dealt with are of the general singular type, with a left invertible transfer matrix function from the control input to the controlled output. All the static and dynamic H/sub 2/ optimal state feedback solutions are constructed and parameterized, and all the eigenvalues of an optimal closed-loop system are characterized. All optimal closed-loop systems share a set of eigenvalues which are termed the optimal fixed modes, which must be assigned among the closed-loop eigenvalues. This set includes a set of optimal fixed decoupling zeros which shows the minimum absolutely necessary number and location of pole-zero cancellations present in any H/sub 2/ optimal design. It is shown that both the sets of optimal fixed modes and optimal fixed decoupling zeros do not vary. >

On maximizing the convergence rate for linear systems with input saturation

In this note, we consider a few important issues related to the maximization of the convergence rate inside a given ellipsoid for linear systems with input saturation. For continuous-time systems, the control that maximizes the convergence rate is simply a bang-bang control. Through studying the system under the maximal convergence control, we reveal several fundamental results on set invariance. An important consequence of maximizing the convergence rate is that the maximal invariant ellipsoid is produced. We provide a simple method for finding the maximal invariant ellipsoid, and we also study the dependence of the maximal convergence rate on the Lyapunov function.

Brief paper: Disturbance tolerance and rejection of linear systems with imprecise knowledge of actuator input output characteristics

In this paper, we study the robustness of linear systems with respect to the disturbances and the uncertainties in the actuator input output characteristics. Disturbances either bounded in energy or bounded in magnitude are considered. The actuator input output characteristics are assumed to reside in a so-called generalized sector bounded by piecewise linear curves. Robust bounded state stability of the closed-loop system is first defined and characterized in terms of linear matrix inequalities (LMIs). Based on this characterization, the evaluation of the disturbance tolerance and disturbance rejection capabilities of the closed-loop system under a given feedback law is formulated into and solved as optimization problems with LMI constraints. The maximal tolerable disturbance is then determined by optimizing the disturbance tolerance capability of the closed-loop system over the choice of feedback gains. Similarly, the design of feedback gain that maximizes the disturbance rejection capability of can be carried out by viewing the feedback gain as an additional free parameter in the optimization problem for the evaluation of the disturbance rejection capability under a given feedback gain.

Entrepreneurship in engineering education

The recent changes in the world and engineering present both challenges and opportunities to the engineering education. Engineering education is changing to meet these challenges. More and more engineering programs strive to include entrepreneurship and innovation, traditionally American values, in the engineering curriculum. In this paper, we present our view on teaching entrepreneurship to future engineers and describe our experience in introducing entrepreneurship in engineering education through an NSF-sponsored pilot program based on collaboration between Stony Brook University and three other major higher education institutions on Long Island.

A direct method of constructing H/sub 2/ suboptimal controllers-continuous-time systems

An H2-suboptimal control problem is defined and analyzed. Then, an algorithm called H2-suboptimal state feedback gain sequence algorithm (Algorithm A1) is developed. Rather than utilizing a perturbation method, which is numerically stiff and computationally prohibitive, Algorithm A1 utilizes a direct eigenvalue assignment method to come up with a sequence of H2-suboptimal state feedback gains. Also, although the sequence of H2-suboptimal state feedback gains constructed by Algorithm A1 depends on a parameter ɛ, the construction procedure itself does not require explicitly the value of the parameter ɛ. Next, attention is focused on constructing a sequence of H2-suboptimal observer-based measurement feedback controllers. Both full-order as well as reduced-order observer-based controllers are developed. For a given H2-suboptimal state feedback gain, a sequence of observer gains for either a full-order or reduced-order observer can be constructed by merely dualizing Algorithm A1. The direct method of constructing H2-suboptimal controllers developed here has a number of advantages over the perturbation method, e.g., it has the ability to design both full-order and reduced-order observer-based controllers while still maintaining throughout the design the computational simplicity of it.

Construction and parameterization of all static and dynamic H 2 -optimal state feedback solutions for discrete-time systems

Abstract This paper considers an H 2 optimization problem via state feedback for discrete-time systems. The class of problems dealt with here has a left invertible transfer matrix function from the control input to the controlled output. The paper constructs and parameterizes all the static and dynamic H 2 -optimal state feedback solutions. Moreover, all the eigenvalues of an optimal closed-loop system are characterized. All optimal closed-loop systems share a set of eigenvalues which are termed the optimal fixed modes . Every H 2 -optimal controller must assign among the closed-loop eigenvalues the set of optimal fixed modes. This set of optimal fixed modes includes a set of optimal fixed decoupling zeros which shows the minimum absolutely necessary number and locations of pole-zero cancellations present in any H 2 -optimal design. Most of the results presented here are analogous to, but not quite the same as, those for continuous-time systems. In fact, there are some fundamental differences between the continuous and discrete-time systems reflecting mainly the inherent nature and characteristics of these systems.

A direct method of constructing H/sub 2/ suboptimal controllers-discrete-time systems

For discrete-time systems, an H2-suboptimal control problem is defined and analyzed. Then, an algorithm called H2-suboptimal state feedback gain sequence (Algorithm A1) is developed. Rather than utilizing a perturbation method, which is numerically stiff and computationally prohibitive, Algorithm A1 utilizes a direct eigenvalue assignment method to come up with a sequence of H2-suboptimal state feedback gains. Also, although the sequence of H2-suboptimal state feedback gains constructed by Algorithm A1 depends on a parameter ɛ, the construction procedure itself does not require explicitly the value of the parameter ɛ. Next, attention is focused on constructing a sequence of H2-suboptimal estimator-based measurement feedback controllers. Three different estimator structures (prediction, current, and reduced-order estimators) are considered. For a given H2-suboptimal state feedback gain, a sequence of estimator gains for any of the three estimators considered can be constructed by merely dualizing Algorithm A1. The direct method of constructing H2-suboptimal controllers developed here has a number of advantages over the perturbation method, e.g., it has the ability to design all three types of estimator-based controllers while still maintaining throughout the design the computational simplicity of it. This paper is the discrete-time version of Ref. 1. There are some conceptual similarities as well as fundamental differences between the H2-suboptimal control problems for continuous-time and discrete-time systems. The fundamental differences arise mainly from the fact that, in contrast to continuous-time systems, for discrete-time systems the infimum of the H2-norm over the class of strictly proper controllers is in general different from the infimum of the H2-norm over the class of proper controllers.

Linear controller for an inverted pendulum having restricted travel-a high-and-low gain approach

The problem of balancing an inverted pendulum has been a benchmark example in demonstrating and motivating various control design techniques. In this paper, we provide a linear state feedback design technique for balancing an inverted pendulum. The pivot of this pendulum is mounted on a carriage which has limited horizontal travel. For any given (arbitrarily small) allowable travel of the carriage, our design yields a linear state feedback controller which balances the pendulum with an infinite amount of gain margin in the sense that, if the feedback gain is perturbed by any multiplying factor greater than one, the controller will still balance the pendulum without requiring greater traveling distance than the maximum allowable motion.