Tomoaki Hashimoto

Probabilistic constrained model predictive control for linear discrete-time systems with additive stochastic disturbances

Model predictive control (MPC) is a kind of optimal feedback control in which the control performance over a finite future is optimized and its performance index has a moving initial time and a moving terminal time. The objective of this study is to propose a design method of MPC for linear discrete-time systems with stochastic disturbances under probabilistic constraints. For this purpose, the two-sided Chebyshevs inequality is applied to successfully handle probabilistic constraints with less computational load. A necessary and sufficient condition for the feasibility of the stochastic MPC is shown here. Moreover, a sufficient condition for the stability of the closed-loop system with stochastic MPC is derived by means of a linear matrix inequality.

Receding Horizon Control With Numerical Solution for Nonlinear Parabolic Partial Differential Equations

The optimal control of nonlinear partial differential equations (PDEs) is an open problem with applications that include fluid, thermal, biological, and chemical systems. Receding horizon control is a kind of optimal feedback control, and its performance index has a moving initial time and a moving terminal time. In this study, we develop a design method of receding horizon control for systems described by nonlinear parabolic PDEs. The objective of this study is to develop a novel algorithm for numerically solving the receding horizon control problem for nonlinear parabolic PDEs. The effectiveness of the proposed method is verified by numerical simulations.

Receding Horizon Control for Hot Strip Mill Cooling Systems

In a hot strip mill, the strip is cooled by spraying water from the top and bottom on the runout table (ROT) before the strip is coiled. The desired mechanical properties and metallurgical structure of the strip are achieved by controlling the cooling rate and temperature of the strip on the ROT. In this paper, we propose a design method of receding horizon control for controlling the temperature of a strip whose mathematical model is described by a nonlinear partial differential equation (PDE). We provide a fast numerical solution method for solving the nonlinear optimization problem for a class of nonlinear PDEs. Moreover, a state observer with an unscented Kalman filter for estimating the inhomogeneously distributed temperature of the strip is incorporated into the receding horizon controller. The effectiveness of the proposed method is verified by numerical simulation.

Output Feedback Stabilization of Linear Time-Varying Uncertain Delay Systems

This paper investigates the output feedback stabilization problem of linear time-varying uncertain delay systems with limited measurable state variables. Each uncertain parameter and each delay under consideration may take arbitrarily large values. In such a situation, the locations of uncertain entries in the system matrices play an important role. It has been shown that if a system has a particular configuration called a triangular configuration, then the system is stabilizable irrespectively of the given bounds of uncertain variations. In the results so far obtained, the stabilization problem has been reduced to finding the proper variable transformation such that an M-matrix stability criterion is satisfied. However, it still has not been shown whether the constructed variable transformation enables the system to satisfy the M-matrix stability condition. The objective of this paper is to show a method that enables verification of whether the transformed system satisfies the M-matrix stability condition.

Receding horizon control with numerical solution for spatiotemporal dynamic systems

Receding horizon control is a kind of optimal feedback control, and its performance index has a moving initial time and a moving terminal time. Spatiotemporal dynamic systems are often described by partial differential equations, and their behavior is characterized by both spatial and temporal variables. In this study, we develop a design method of receding horizon control for a generalized class of spatiotemporal dynamic systems. Using the variational principle, we first derive the exact stationary conditions that must be satisfied for a performance index to be optimized. Next, we provide a numerical algorithm for solving the stationary conditions via finite-dimensional approximation. Finally, the effectiveness of the proposed method is verified by numerical simulations.

Controllability and Observability of Linear Time-Invariant Uncertain Systems Irrespective of Bounds of Uncertain Parameters

In this paper, the controllability and observability of linear time-invariant uncertain systems are investigated. The systems under consideration contain time-invariant uncertain parameters that may take arbitrarily large values. In such a situation, the locations of uncertain parameters in system matrices play an important role. We examine the permissible locations of uncertain parameters in system matrices for a linear uncertain system to be controllable and observable independently of the bounds of the uncertain parameters. The objective of this paper is to show that a linear uncertain system is controllable and observable, irrespective of the bounds of uncertain parameters, if and only if the system has a particular configuration called a complete generalized antisymmetric stepwise configuration (CGASC). Furthermore, the dual configuration of a CGASC is introduced and studied here.

Controlling Large-Scale Self-Organized Networks with Lightweight Cost for Fast Adaptation to Changing Environments

Self-organization has potential for high scalability, adaptability, flexibility, and robustness, which are vital features for realizing future networks. Convergence of self-organizing control, however, is slow in some practical applications compared to control with conventional deterministic systems using global information. It is therefore important to facilitate convergence of self-organizing controls. In controlled self-organization, which introduces an external controller into self-organizing systems, the network is controlled to guide systems to a desired state. Although existing controlled self-organization schemes could achieve this feature, convergence speed for reaching an optimal or semioptimal solution is still a challenging task. We perform potential-based self-organizing routing and propose an optimal feedback method using a reduced-order model for faster convergence at low cost. Simulation results show that the proposed mechanism improves the convergence speed of potential-field construction (i.e., route construction) by at most 22.6 times with low computational and communication cost.

Stabilization of reaction-diffusion equations with state delay using boundary control input

This study analyses a stabilization method for reaction-diffusion equations with state delay using boundary control input. The proposed control strategy is based on the backstepping method, wherein the controlled system is transformed into a target system. The objective of this study is to show that the conventional transformation, which was proposed for undelayed reaction-diffusion equations, can still provide a stabilizing boundary controller for a special class of delayed equations.

Receding horizon control for a class of discrete-time nonlinear implicit systems

Receding horizon control is a type of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial time and terminal time. Implicit systems belong to a more generalized class of systems than a class of explicit systems, because they can additionally contain algebraic constraints. The objective of this study is to develop a novel design method of receding horizon control for a generalized class of discrete-time nonlinear implicit systems. Using the variational principle, we derive the stationary conditions that must be satisfied for a performance index to be optimized. Moreover, we provide numerical algorithms for solving the obtained stationary conditions. Next, we establish the stability criterion for the closed-loop system with the proposed method. Finally, the effectiveness of the proposed method is verified by numerical simulations.

Output Feedback receding horizon control for spatiotemporal dynamic systems

Receding horizon control problem is investigated here for a generalized class of spatiotemporal dynamic systems. Receding horizon controllers often assume that all state variables are exactly known. However, it is usual that the state variables of systems are measured through outputs, hence, only limited parts of them can be used directly. Moreover, the output signals may be disturbed by process and sensor noises. In this study, we develop a design method of output feedback receding horizon control for a generalized class of spatiotemporal dynamic systems. We apply the contraction mapping method and unscented Kalman filter for solving the optimization and estimation problems, respectively. The effectiveness of the proposed method is verified by numerical simulations.