Shun-ichi Azuma

Optimal dynamic quantizers for discrete-valued input control

This paper discusses an optimal design problem of dynamic quantizers for a class of discrete-valued input systems, i.e., linear time-invariant systems actuated by discrete-valued input signals. The quantizers considered here are in the form of a linear difference equation, for which we find a quantizer such that the system composed of a given linear plant and the quantizer is an optimal approximation of the given linear plant in the sense of the input-output relation. First, we derive a closed form expression for the performance of a class of dynamic quantizers. Next, based on the performance analysis, an optimal dynamic quantizer and its performance are provided. This result further shows that even for such discrete-valued input systems, a controller can be easily designed by the existing tools for the linear system design such as robust control theory. Finally, the relation among the optimal dynamic quantizer and two other quantizers, i.e., the receding horizon quantizer and the @D@S modulator, is discussed.

Synthesis of Optimal Dynamic Quantizers for Discrete-Valued Input Control

This paper presents an optimal dynamic quantizer synthesis method for controlling linear time-invariant systems with discrete-valued input. The quantizers considered here include dynamic feedback mechanism, for which we find quantizer parameters such that the system composed of a given linear plant and the quantizer is an optimal approximation of the linear plant in terms of the input-output relation. First, the performance of an arbitrarily given dynamic quantizer is analyzed, where we derive a closed form expression of the performance. Based on this result, it is shown that the quantizer design is reduced to a nonconvex optimization problem for which it is hard to obtain a solution in a direct way. We obtain a globally optimal solution, however, by taking advantage of a special structure of the problem which allows us to relax the original nonconvex problem. The resulting problem is easy to solve, so we provide a design method based on linear programming and derive an optimal structure of the dynamic quantizers. Finally, the validity of the proposed method is demonstrated by numerical examples.

Stochastic Source Seeking by Mobile Robots

We consider the problem of designing controllers to steer mobile robots to the source (the minimizer) of a signal field. In addition to the mobility constraints, e.g., posed by the nonholonomic dynamics, we assume that the field is completely unknown to the robot and the robot has no knowledge of its own position. Furthermore, the unknown field is randomly switching. In the case where the information of the field (e.g., the gradient) is completely known, standard motion planning techniques for mobile robots would converge to the known source. In the absence of mobility constraints, convergence to the minimum of unknown fields can be pursued using the framework of numerical optimization. By considering these facts, this paper exploits an idea of the stochastic approximation for solving the problem mentioned in the beginning and proposes a source seeking controller which sequentially generates the next waypoints such that the resulting discrete trajectory converges to the unknown source and which steers the robot along the waypoints, under the assumption that the robot can move to any point in the body fixed coordinate frame. To this end, we develop a rotation-invariant and forward-sided version of the simultaneous-perturbation stochastic approximation algorithm as a method to generate the next waypoints. Based on this algorithm, we design source seeking controllers. Furthermore, it is proven that the robot converges to a small set including the source in a probabilistic sense if the signal field switches periodically and sufficiently fast. The proposed controllers are demonstrated by numerical simulations.

Controllability Analysis of Biosystems Based on Piecewise-Affine Systems Approach

This paper discusses the controllability problem of biosystems based on the piecewise-affine system model representation. First, we consider what kind of controllability problems are useful for analyzing and controlling biosystems, and then the controllable set problem, that is, a problem of finding a state set in which each state can be driven to a given target state, is formulated. It is shown that this problem will be very useful for many kinds of problems on control of biosystems such as the input allocation problem and the stabilization problem. Next, based on our previous probabilistic controllability analysis technique for hybrid dynamical systems, a more sophisticated method for solving the above complex problem in an approximated and suitable way for biosystem analysis is proposed. Finally, the proposed framework is applied to the quorum sensing system of the pathogen Pseudomonas aeruginosa for explaining how it is formulated and what solutions are obtained.

An optimal dynamic quantizer for feedback control with discrete-valued signal constraints

This paper addresses a problem of finding an optimal dynamic quantizer in a given feedback control loop with discrete-valued signal constraints. First, an upper bound of the performance of dynamic quantizers is derived as a closed form. Based on this, we next provide an optimal dynamic quantizer, which is a solution to the problem, in an analytical way. Finally, the validity of the optimal dynamic quantizer is demonstrated by a numerical simulation.

Distributed Controllers for Multi-Agent Coordination Via Gradient-Flow Approach

This paper provides a unified solution for a general distributed control problem of multi-agent systems based on the gradient-flow approach. First, a generalized coordination is presented as a control objective which represents a wide range of coordination tasks (e.g., consensus, formation and pattern decision) in a unified manner. Second, a necessary and sufficient condition for the gradient-based controllers to be distributed is derived. It turns out that the notion of clique (i.e., complete subgraph) plays a crucial role to obtain any distributed controllers. Furthermore, all such controllers are explicitly characterized with free design parameters. Third, it is shown how to choose an optimal controller in a systematic way among all distributed ones, where an optimality measure is introduced for the generalized coordination. Finally, the effectiveness of the proposed method is demonstrated through simulations, where a distributed pattern decision is discussed as an example of the generalized coordination.

Performance analysis of model-free PID tuning of MIMO systems based on simultaneous perturbation stochastic approximation

Abstract This paper addresses the performance comparison of simultaneous perturbation stochastic approximation (SPSA) based methods for PID tuning of MIMO systems. Four typical SPSA based methods, which are one-measurement SPSA (1SPSA), two-measurement SPSA (2SPSA), Global SPSA (GSPSA) and Adaptive SPSA (ASPSA) are examined. Their performances are evaluated by extensive simulation for several controller design examples, in terms of the stability of the closed-loop system, tracking performance and computation time. In addition, the performance of the SPSA based methods are compared to the other stochastic optimization based approaches. It turns out that the GSPSA based algorithm is the most practical in terms of the stability and the tracking performance.

Optimal control of sampled-data piecewise affine systems and its application to CPU processing control

This paper addresses the optimal control problem of the continuous-time piecewise affine (PWA) systems with autonomous switching executed at each sampling time, which we call sampled-data PWA systems. In particular, an optimal continuous-time controller is derived for a more general class of sampled-data PWA systems, which are controllable but whose subsystems in some modes may be uncontrollable in the usual sense. Furthermore, as an application of this approach, we formulate the high-speed and energy-saving control problem of the CPU processing, and show the validity of the approach.

Dynamic Quantization of Nonlinear Control Systems

This paper addresses a problem of finding an optimal dynamic quantizer for nonlinear control subject to discrete-valued signal constraints, i.e., to the condition that some signals must take a value on a discrete and countable set at each time instant. The quantizers to be studied are in the form of a nonlinear difference equation which maps continuous-valued signals into discrete-valued ones. They are evaluated by a performance index expressing the difference between the resulting quantized system and the unquantized system, in terms of the input-output relation. In this paper, we present a closed-form solution, which globally minimizes the performance index. This result shows the performance limitation of a general class of dynamic quantizers. In addition to this, some results on the structure and the stability are given in order to clarify the mechanism of the best dynamic quantization in nonlinear control systems.

Model predictive control for optimally scheduling intermittent androgen suppression of prostate cancer

Mathematical modeling of prostate cancer under intermittent androgen suppression revealed that we may be able to delay relapse by optimally scheduling the hormone therapy for each patient. However, our previous study showed the difficulty of the scheduling by minimizing the maximal tumor growth rate because the transient dynamics is also important and can help to delay the relapse for a finite time. Here, we propose to use model predictive control for scheduling intermittent androgen suppression. We find that model predictive control tends to delay the relapse of prostate specific antigen more than the method with minimizing the maximal tumor growth rate. Therefore, model predictive control is a promising approach for practically applying the mathematical model to optimally schedule intermittent androgen suppression.