This paper considers the output feedback H 2 guaranteed cost control problem. In [1], it was observed that exploiting the solution of a discrete algebraic Riccati equation corresponding to an optimal full information control design allowed the output feedback control problem, for a fixed value of a design parameter, to be reduced to a so-called full control problem in which only filter gains of an estimator needed to be designed. However, this critical result was not proved. This paper proves this result.

This paper examines methods to calculate a rank-one approximation using the SVD within a feedback control loop. The rank-one approximation obtained permits the control of mxn subsystems using m+n inputs. The feedback loop presents opportunities to speed up the calculation of this approximation by using information from the previous sample time. This paper will explain some modifications to the Power Method and Jacobi Method, as well as demonstrate and discuss the pros and cons of the various techniques.

A new methodology for parametric sensitivity based robust optimal control sysnthesys (PS-ROCS), is presented for robust optimal control synthesis using augmented plant dynamics with sensitivity co-system. Robustness of the control system to parametric uncertainties is ensured by minimizing the energy in the states where state vector incorporates states of the sensitivity co-system. The sensitivity dynamics is developed for the first-order parametric sensitivities from the system dynamics. This paper uses the Youla parameterization approach for controller synthesis. The robust optimal design methodology is demonstrated using a linearized model of double slider mechanism. For comparative study, two control designs obtained using the proposed methodology is compared with the H ∞ -based design. It was observed that the new methodology presents a viable alternative for robust optimal control design. The attractiveness of the proposed approach lies in the fact that no uncertainty estimates are needed as parametric sensitivities are directly minimized.

This paper focuses on a low order robust stabilizer design for linear time varying (LTV) internal model based system in the discrete time domain. While adopting the output feedback gain injection based stabilization structure for continuous LTV systems, the discrete stabilization synthesis has its unique challenges, and the approach formulated in the continuous domain cannot be directly applied. Therefore, in this paper, the stabilization for LTV internal model based control in the discrete setting is formulated. Its challenges are revealed and methods to convert it into a convex optimization based synthesis are proposed. The approach is then validated through simulation analysis and experimental investigations.

In this paper, the output covariance constraint (OCC) control problem is cast as a convex optimization with linear matrix inequality (LMI) constraints. The OCC control problem is an optimal control problem that is concerned with minimizing control effort subject to multiple performance constraints on output covariance matrices. The contribution of this paper is the characterization of the control synthesis LMIs used to solve the OCC control problem. To demonstrate the effectiveness of the proposed approach a numerical example is solved with the control synthesis LMIs. The LMI solutions are then compared to results obtained when using the original iterative OCC algorithm. Both discrete and continuous-time problems are considered.

This paper discusses the recently developed time-varying internal model-based tracking control design. In particular, it is shown that the parallel connection between the stabilizer and the internal model would facilitate the design of a robust stabilizer. Also it is shown that in the presence of plant model uncertainty the time-varying internal model based on the nominal values of the plant model can generate an input which can be made close enough to the desired control input rendering the regulated error identically zero. The simulation results validate the proposed robust stabilizer design.

This paper is concerned with the synthesis of static output feedback (SOF) control satisfying multi-objective H 2 /H ∞ performance for LTI systems. Given an initially stabilizing SOF gain K o , an estimate of the set of stabilizing gains is obtained using Monte Carlo based randomized search. A synthesis algorithm which combines both linear matrix inequalities (LMIs) and genetic algorithms (GA) is proposed. To improve the efficiency of this hybrid algorithm, the GA employs a projection-like operation so that the solution candidates lie in the interior of the set of stabilizing gains in a neighborhood of K o .

This paper presents, for discrete-time LTI systems with unstructured dynamic uncertainty, a methodology for designing full information controllers which minimize the upper bound on robust H2 performance given in [1]. It is first shown that this optimal control problem can be cast as a semi-definite program. Then, it is shown that this optimization problem can be solved efficiently and accurately using discrete algebraic Riccati equations.

This paper presents a theoretical design of how a minimax equilibrium of differential game is achieved in a class of large-scale nonlinear dynamic systems, namely the recurrent neural networks. In order to realize the equilibrium, we consider the vector of external inputs as a player and the vector of internal noises (or disturbances or modeling errors) as an opposing player. The purpose of this study is to construct a nonlinear H ∞ optimal control for deterministic noisy recurrent neural networks to achieve an optimal-oriented stabilization, as well as to attenuate noise to a prescribed level with stability margins. A numerical example demonstrates the effectiveness of the proposed approach.

As a continuation of our study, this paper extends our research results of optimality-oriented stabilization from deterministic recurrent neural networks to stochastic recurrent neural networks, and presents a new approach to achieve optimally stochastic input-to-state stabilization in probability for stochastic recurrent neural networks driven by noise of unknown covariance. This approach is developed by using stochastic differential minimax game, Hamilton-Jacobi-Isaacs (HJI) equation, inverse optimality, and Lyapunov technique. A numerical example is given to demonstrate the effectiveness of the proposed approach.

In this paper, a problem of designing a switched tracking dynamic output-feedback controller for uncertain systems is considered. The design problem amounts to solving an optimization problem, the cost function of which is neither smooth nor convex. By applying the proposed method to a nominal switched controller design methods, we designed a switched robust controller. Advantages of the method demonstrated through an example.

In this paper a graphical design method is introduced for finding all proportional integral (PI) controllers that stabilize a single area non-reheat steam generation unit for a range of plant parameters. This problem is solved by finding all achievable PI controllers that robustly stabilize the system. Additive uncertainty modeling is used to describe the uncertain perturbed system. A key advantage of this procedure is that it depends only on the frequency response of the system and does not require the plant transfer function coefficients.

In this paper a graphical technique is introduced for finding all continuous-time or discrete-time proportional integral derivative (PID) controllers that satisfy a weighted sensitivity constraint of an arbitrary order transfer function with time delay. These problems can be solved by finding all achievable PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. The key advantage of this procedure is that this method depends only on the frequency response of the system. The delta operator is used to describe the controllers in a discrete-time model, because it not only possesses numerical properties superior to the discrete-time shift operator, but also converges to the continuous-time controller as the sampling period approaches zero. A unified approach allows us to use the same procedure for discrete-time and continuous-time weighted sensitivity design of PID controllers.

In this work, a Linear Parameter-Varying (LPV) control method is used to compensate the hysteretic behavior of a Shape Memory Alloy (SMA) wire. Controller is implemented on an experimental system which consists of a pre-tension spring and a mass actuated with a thin SMA wire. The hysteretic characteristic of the SMA wire is modeled using the Preisach model and the model is verified both for the major and minor hysteresis loops. The small signal linear gain of the Preisach model is used as a scheduling stiffness variable. The parameter-dependent controller is scheduled based on the real time measurement of the stiffness variable. An H ∞ controller is also synthesized by representing the hysteresis as a parametric uncertainty and comparisons are made with LPV gain scheduling controllers using similar weights for both controllers. Experimental trajectory tracking results show that the LPV Gain Scheduling controller has a better response and the hysteresis uncertainty is compensated for the full range of stiffness variability.

This paper presents a methodology for analyzing the H 2 guaranteed cost performance of a discrete-time LTI system with unstructured dynamic uncertainty. Using the methods of guaranteed cost control, an upper bound on H 2 guaranteed cost performance over unstructured parametric uncertainty is formulated in terms of feasibility of a linear matrix inequality. It is then shown that the feasibility of this inequality also guarantees the same level of performance also over unstructured dynamic uncertainty. This is then used to formulate the problem of finding the best upper bound on H 2 guaranteed cost performance over unstructured causal dynamic uncertainty as a semi-definite program. Finally, it is shown that this optimization problem can be solved efficiently and accurately using discrete algebraic Riccati equations.

For sampled-data control systems, where a continuous-time plant is under digital control, one of the most important design parameter is the sample rate/period. Higher sample rate typically is associated with the need of high performance components and processors that results in higher system cost. In this paper, we propose an approach to determine the slowest sample rate for a sampled-data control system that will achieve the desired performance and robustness specifications. An optimization problem can be formulated using lifting technique to parameterize sample period for a sampled-data control system. The utility of the proposed approach is numerically verified through the control systems design of the media advance system of an inkjet printer.

The brief instability concept in Linear Parameter Varying (LPV) systems allows the linear system to be unstable for some values of the LPV parameters so that instability occurs only for a short period of time. The present paper takes advantage of an extension of the notion of the brief instability to the LPV systems with time-delay in their dynamics to examine the performance degradation in Fault Tolerant Control (FTC) systems in the presence of false identification of the fault signals. The paper provides tools for the stability and performance analysis of such systems, where performance is evaluated in terms of induced L 2 -gain. The results presented in the paper demonstrate that stability and performance can be evaluated by examining the feasibility of a parameterized set of Linear Matrix Inequalities (LMIs). The paper provides the analysis conditions to guarantee the asymptotic stability and H ∞ performance for FTC systems, in which instability, due to the false identification of the fault signals, is allowed to take place for a short period of time. A numerical example is presented to illustrate the qualifications of the proposed analysis and synthesis conditions for treating brief instability in the delayed FTC systems.