Yasumasa Fujisaki

Probabilistic design of LPV control systems

This paper presents an alternative approach to design of linear parameter-varying (LPV) control systems. In contrast to previous methods, which are focused on deterministic algorithms, this paper is based on a probabilistic setting. The proposed randomized algorithm provides a sequence of candidate solutions converging with probability one to a feasible solution in a finite number of steps. The main features of this approach are as follows: (i) The randomized algorithm gives a method for general LPV plants with state space matrices depending on scheduling parameters in a nonlinear manner. That is, the probabilistic setting does not need a gridding of the set of scheduling parameters or approximations such as a linear fractional transformation of the state space matrices. (ii) The proposed algorithm is sequential and, at each iteration, it does not require heavy computational effort such as solving simultaneously a large number of linear matrix inequalities.

Probabilistic robust design of LPV control systems

Presents an alternative approach to solve robust performance problems for linear parameter-varying (LPV) control systems. In contrast to previous methods, which are focused on deterministic algorithms, this paper is based on a probabilistic setting. The proposed randomized algorithm provides a sequence of candidate solutions converging with probability one to a feasible solution in a finite number of steps. The main advantages of this method over the previous literature are as follows: (i) the randomized algorithm gives a direct method for general LPV plants with state-space matrices depending on scheduling parameters in a nonlinear manner, i.e. the probabilistic setting does not require any approximation, such as a linear fractional transformation (LFT), of the state space matrices or a gridding on the set of scheduling parameters; (ii) the proposed algorithm is sequential and, at each iteration, it does not require heavy computational effort, such as simultaneously solving a large number of linear matrix inequalities.

Mixed Deterministic/Randomized Methods for Fixed Order Controller Design

In this paper, we propose a general methodology for designing fixed order controllers for single-input single-output plants. The controller parameters are classified into two classes: randomized and deterministically designed. For the first class, we study randomized algorithms. In particular, we present two low-complexity algorithms based on the Chernoff bound and on a related bound (often called ldquolog-over-logrdquo bound) which is generally used for optimization problems. Secondly, for the deterministically designed parameters, we reformulate the original problem as a set of linear equations. Then, we develop a technique which efficiently solves it using a combination of matrix inversions and sensitivity methods. A detailed complexity analysis of this technique is carried on, showing its superiority (from the computational point of view) to existing algorithms based on linear programming. In the second part of the paper, these results are extended to H infin performance. One of the contributions is to prove that the deterministically designed parameters enjoy a special convex characterization. This characterization is then exploited in order to design fixed order controllers efficiently. We then show further extensions of these methods for stabilization of interval plants. In particular, we derive a simple one-parameter formula for computing the so-called critical frequencies which are required by the algorithms.

Brief paper: Guaranteed cost regulator design: A probabilistic solution and a randomized algorithm

This paper presents a gradient-based randomized algorithm to design a guaranteed cost regulator for a plant with general parametric uncertainties. The algorithm either provides with high confidence a probabilistic solution that satisfies the design specification with high probability for a randomly sampled uncertainty or claims that the feasible set of the design parameters is too small to contain a ball with a given radius. In both cases, the number of iterations executed in the algorithm is of polynomial order of the problem size and is independent of the dimension of the uncertainty.

Probabilistic robust controller design: probable near minimax value and randomized algorithms

This paper presents a probabilistic approach to robust controller design. This design can be recast as a minimax problem with a cost function. In order to solve the problem efficiently, the definition of probable near minimax value is introduced. A probable near minimax value of the function can be calculated with a certain accuracy and a certain confidence by using a randomized algorithm, where independent identically distributed samples of optimized parameters are generated according to probability measures. It is shown that the necessary number of the samples depends on the accuracy and the confidence and is independent of the number of the parameters. Furthermore, a special case such that the cost function has a global saddle point is investigated. The definition of probable near saddle value, which is weaker than that of probable near minimax value, is introduced. Then, it is shown that the necessary number of samples is smaller in this case.

Decentralized H/sub /spl infin// controller design for large-scale systems: a matrix inequality approach using a homotopy method

This paper considers a decentralized H/sub /spl infin// control problem for large-scale systems consisting of a number of interconnected subsystems with the information structure constraints which are compatible with the subsystems. The H/sub /spl infin// control specification is imposed on the transfer function from the disturbance input to the controlled output of the overall closed-loop system. The decentralized H/sub /spl infin// control problem is reduced to a feasibility problem of a bilinear matrix inequality (BMI). To solve the BMI, an algorithm is proposed using the idea of the homotopy method, where the interconnections between subsystems are increased gradually from zeros to the given magnitudes. The case where polytopic perturbations exist in the interconnections is also treated.

Reliable decentralised stabilisation of multi-channel systems: a design method via dilated LMIs and unknown disturbance observers

Reliable decentralised stabilisation is considered for general multi-channel plants, where the objective is to maintain stability of the closed-loop system when all of decentralised controllers work together and when one of the controllers is extracted due to a failure. For this control problem, a design method is presented, where a dilated LMI technique is employed for deriving reliable state feedback design, while a version of unknown disturbance observer is used as a decentralised observer for extending the design to output feedback case. Applicability of the proposed method is demonstrated through a power system example, where a model reduction and a low pass filter are further employed.

System Representation and Optimal Control in Input-Output Data Space

Abstract Optimal control is considered for a linear time-invariant plant in the input-output data space. The proposed control strategy does not employ any traditional mathematical model such as a transfer function or a state-space equation. Instead, the plant dynamics is represented as a set of basis vectors whose elements are input-output data of the plant. Using this system representation, two optimal control problems are solved. One is to find the control input which minimizes a quadratic performance index. The other is to find the control input which minimizes a quadratic performance index subject to achieving dead-beat tracking.

Optimal preview control based on quadratic performance index

This paper revisits the optimal preview tracking problem based on quadratic performance index. The reference signal is assumed to be step-type and previewable in a fixed interval of time ahead. Then, a reasonable performance index which quantifies the effect of the preview action on the transient response to the reference signal is proposed for this problem. The optimal preview control law is derived using optimal regulator theory. It consists of the feedback from the state of the plant and the feedforward from the reference signal within the previewable time interval. The relationship between the feedforward gains and the preview action is also investigated. Furthermore, a two-degree-of-freedom preview servosystem is proposed, in which the servo compensator is effective only when there exist modeling errors or disturbance inputs. This servosystem guarantees that designing the nominal transient response to the reference signal is independent of the gain of the servo compensator.

A two-degree-of-freedom design of optimal servosystems

A two-degree-of-freedom design of optimal servosystems for reference signals of step functions is proposed. An optimal tracking problem is considered as an optimal regulator problem for a variation system that is defined around the steady state determined by the reference signal. An integral compensator is applied to the resultant control system in order to cope with modeling errors of the plant and constant disturbance inputs to the plant. To preserve the optimal tracking property for reference signals, complementary state feedback is used to cancel the effect of the integral compensation in the ideal case of no modeling error and no disturbance input.<<ETX>>