Shintaro Ishijima

Robust stabilization of a system with delays in control

A robust stabilization problem is discussed for a system with delays in control. The authors derive a robust stabilizing law against additive perturbations. Then, motivated by the feature of predictive controllers, they investigate the structure of robust stabilizing law and provide some interpretations on the relation between the value of time delay and the achievable margin of robust stabilizability. >

Brief H∞ performance of preview control systems

Performance of the preview control is investigated in terms of H^~-criterion. In the infinite-horizon time setting, the limitation of H^~ performance in preview control action is characterized with the Hamiltonian matrix. By employing the property of Hamiltonian matrix, the solvability and analytic solution for the preview full-information control problem are clarified based on an auxiliary introduced matrix Riccati equation. The property of resulting control law is illustrated with a numerical example.

Robust controller design for delay systems in the gap-metric

A robust stabilization problem in the gap-metric is discussed for a system with delays in control. The authors derive a design procedure of robust controllers based on finite-dimensional Ricatti equations and it is shown that the resulting controller has a structure of observer-based predictive action. By employing completing the square argument, a game theoretic interpretation is also provided on the trade-off between the initial-uncertainties and attenuating the disturbance caused by plant uncertainties. >

LQ preview synthesis: optimal control and worst case analysis

A generalized LQ-control problem, which treats a mixed attenuation of stored disturbance and initial state uncertainty, is discussed in the infinite-horizon time setting. The posed problem covers a part of predictive control problems and enables one to deal with the LQ optimal preview servocontroller design. For the generalized LQ problem, we first derive an optimal preview control which minimizes the LQ cost functional and provide some interpretations on the structure of resulting control law. We then analyze worst case initial uncertainties, i.e., those of initial state and the shape of stored disturbance, which maximize the cost functional of the resulting closed-loop system.

Formulas on Preview and Delayed

A generalized Hinfin control problem, which covers preview and delayed control strategies, is discussed based on a state-space approach. By introducing a Hamiltonian matrix, which is associated with a delay-free generalized plant, the analytic solution to the corresponding operator Riccati equation is newly established. Based on the result obtained here, the Hinfin control problem is solved and, for typical control problems (e.g., Hinfin and linear quadratic (LQ) control for multiple input delay systems, Hinfin preview control), some interpretations are provided on the resulting control system

H^{\infty}

Abstract In the synthesis of tracking control systems, the compensation signal, which is applied in the finite-horizon time, is effective for improving the performance of controlled system. In this paper, a design method of finite-horizon compensation signal and optimal internal state of controller are discussed for stabilized systems. By characterizing the singular-value problem for correspondingly defined Hankel operator, it is shown that the internal state and the compensation signal, which attains favorable transient, is constructively given based on the combination of singular vectors. The strength and the limitation of applying the compensation signal are illustrated with numerical examples.

Control

A backstepping-like design approach for reduced-order nonlinear observers is proposed. The basic idea of this approach is as follows. First, an appropriate function of the state variables to be estimated is constructed. The next function of the state variables to be estimated is then derived by designing the previous nonlinear function observer. Finally the procedure terminates, resulting in a partial differential equation to be solved. If the resultant differential equation is solvable, then the observer can be calculated. The connection between observers with linear error dynamics and this approach is discussed.

IMPROVING TRANSIENT WITH COMPENSATION LAW

Abstract A robust stabilization problem is discussed for a system with delays in control. We derive a robust stabilizing law against the uncertainties such as additive/multiplicative perturbations. Motivated by the feature of predictive controllers, we also provide some interpretations on the structure of the required control law.

Design of nonlinear observer by a backstepping approach

Dynamics of the mechanical system is described by the matrix-second-order differential equation, and the coefficient matrices in the equation have some special properties such as symmetry and positivity. These properties should be reflected to the design method of controllers for mechanical systems. In this paper we discuss control problems of mechanical systems in the matrix-second-order differential equation model by paying attention to their potential and kinetic energy. First we introduce a concept called generalized energy function and then by using this new concept we discuss observability and controllability and propose a design method of feedback controllers of the mechanical systems.

Robust Stabilization Problem for a System with Delays in Control

Abstract Properties of Hankel operator are discussed for a system with delays in state. In the finite-time horizon setting, the Hankel singular values are characterized by the roots of transcendental equation and the singular vectors are constructively given based on the solution to differential equation. Then, employing the singular vectors for the base of state-space, we elaborate a calculation method of finite-dimensional approximation.