Joe Imae

A Riccati-equation-based algorithm for nonlinear optimal control problems

In this paper, we propose an iterative method for numerical solutions of unconstrained nonlinear optimal control problems, which is essentially based on the closed loop solutions of the linear quadratic optimal control problems. We also prove that accumulation points generated by the algorithm, if they exist, satisfy the weak necessary conditions for optimality. Moreover, we illustrate the numerical effectiveness of the present algorithm through five examples by simulation.

A design method for nonlinear H/sub /spl infin// control systems via Hamilton-Jacobi-Isaacs equations: a genetic programming approach

We deal with the design problem of feedback control synthesis via Hamilton-Jacobi-Isaacs (H-J-I) equations. Making use of the emergent property of genetic programming (GP), we propose an approach for obtaining the solution of H-J-I equations approximately. Some numerical examples are demonstrated to illustrate the practicability of the proposed method.

H ∞ norm computation for LTV systems using nonlinear optimal control algorithms

We discuss the computation for ℒ2-induced norms of finite-horizon linear time-varying systems. It is well known that ℒ2-induced norm calculating problems can be converted into optimal control problems. So, with the help of optimal control algorithms, we propose a numerical technique for ℒ2-induced norm computation. Our approach is as follows. First, we present a new computational method for nonlinear optimal control problems that is numerically reliable, stable and robust, analysing the convergence property under some assumptions. Next, by modifying the presented method, we propose an algorithm for the ℒ2-induced norm calculation of finite-horizon linear time-varying systems, which is essentially different from all other existing methods. Finally, the effectiveness of our algorithm is demonstrated by simulation.

L/sub 2/-gain computation for nonlinear systems using optimal control algorithms

We focus on the computation for the L/sub 2/-gain of nonlinear systems over a finite horizon. Based on the similarity between L/sub 2/-gain calculation problems and optimal control problems, we present a new computational algorithm for L/sub 2/-gain of nonlinear systems. We also prove that accumulation points generated by the algorithm, if they exist, satisfy the necessary conditions for optimality derived from the L/sub 2/-gain calculation problems. Lastly, the effectiveness of the algorithm is demonstrated through some simulations.

A Riccati‐equation‐based algorithm for continuous‐time optimal control problems

In this paper we consider continuous-time unconstrained optimal control problems. We propose a computational method which is essentially based on the closed-loop solutions of the linear quadratic optimal control problems. In the proposed algorithm, Riccati differential equations play an important role. We prove that accumulation points generated by the present algorithm, if they exist, satisfy the weak necessary conditions for optimality, under some assumptions including Kalmans sufficient conditions for the bounded Riccati solutions. In addition, we also propose the simple but effective technique to guarantee the boundedness of the solutions of Riccati equations. Lastly, we illustrate the usefulness of the present algorithm through simulation experiences. Copyright

A simple numerical method for minimizing the maximum eigenvalues of symmetric matrices via nonlinear differential equation solvers

In this paper, we present a simple numerical method for solutions of linear/bilinear matrix inequalities (LMI/BMI) problems, more exactly a method for minimizing the maximum eigenvalues of real valued symmetric matrices. Nonlinear differential equation solvers are used in our approach. First, we convert the non-differentiable minimization problem for the maximum eigenvalues into one of differentiable optimization problems by means of interior point methods. Second, making use of differential equation solvers, we present a simple method for finding the solutions of the optimization problems. Finally, we demonstrate the effectiveness of the algorithm through some simulation experiences.

A chattering control based algorithm for nonlinear optimal control problems with control-constraints

Based on the concept of chattering controls, originally given by Gamkrelidze (1965), we propose a new algorithm for nonlinear optimal control problems with constraints on control. Note that these problems include optimal control problems using quantized controls. We prove that accumulation points generated by the proposed algorithms, if they exist, satisfy the maximum principle. Moreover, we demonstrate the implementability of the algorithm by simulation experiments.

L/sub 2/-induced norm computation via nonlinear optimal control algorithms

In this paper, we discuss the computation for L/sub 2/-induced norms of finite-horizon linear time-varying systems. Based on optimal control algorithms, we propose a new algorithm for the L/sub 2/-induced norm computation. Its convergence property is proved, and the effectiveness of our method is also demonstrated through several simulations.<<ETX>>