Closed-Loop Subspace Identification for Stable/Unstable Systems using Data Compression and Nuclear Norm Minimization

This paper provides a subspace method for closed-loop identification, which clearly specifies the model order from noisy measurement data. The method can handle long I/O data of the target system to be noise-tolerant and determine the model order via nuclear norm minimization. First, the proposed method compresses the long data by projecting them to an appropriate low dimensional subspace, then obtains a low order model whose order is specified by a combination of data compression and nuclear norm minimization. Its effectiveness is demonstrated through detailed numerical examples

Actively Learning Gaussian Process Dynamical Systems Through Global and Local Explorations

Usually learning dynamical systems by data-driven methods requires large amount of training data, which may be time consuming and expensive. Active learning, which aims at choosing the most informative samples to make learning more efficient is a promising way to solve this issue. However, actively learning dynamical systems is difficult since it is not possible to arbitrarily sample the state-action space under the constraint of system dynamics. The state-of-the-art methods for actively learning dynamical systems iteratively search for an informative state-action pair by maximizing the differential entropy of the predictive distribution, or iteratively search for a long informative trajectory by maximizing the sum of predictive variances along the trajectory. These methods suffer from low efficiency or high computational complexity and memory demand. To solve these problems, this paper proposes novel and more sample-efficient methods which combine global and local explorations. As the global exploration, the agent searches for a relatively short informative trajectory in the whole state-action space of the dynamical system. Then, as the local exploration, an action sequence is optimized to drive the system’s state towards the initial state of the local informative trajectory found by the global exploration and the agent explores this local informative trajectory. Compared to the state-of-the-art methods, the proposed methods are capable of exploring the state-action space more efficiently, and have much lower computational complexity and memory demand. With the state-of-the-art methods as baselines, the advantages of the proposed methods are verified via various numerical examples

Value iteration with deep neural networks for optimal control of input-affine nonlinear systems

This paper proposes a new algorithm with deep neural networks to solve optimal control problems for continuous-time input nonlinear systems based on a value iteration algorithm. The proposed algorithm applies the networks to approximating the value functions and control inputs in the iterations. Consequently, the partial differential equations of the original algorithm reduce to the optimization problems for the parameters of the networks. Although the conventional algorithm can obtain the optimal control with iterative computations, each of the computations needs to be completed precisely, and it is hard to achieve sufficient precision in practice. Instead, the proposed method provides a practical method using deep neural networks and overcomes the difficulty based on a property of the networks, under which our convergence analysis shows that the proposed algorithm can achieve the minimum of the value function and the corresponding optimal controller. The effectiveness of the proposed method even with reasonable computational resources is demonstrated in two numerical simulations

Locally deforming continuation method based on a shooting method for a class of optimal control problems

This paper proposes a new continuation method for solving optimal control problems. The proposed method is based on a shooting method. In the proposed method, a cost function of an optimal control problem is locally deformed to find the solution of the problem in a stable way. This paper also analyses a relationship between the variation of the continuation parameter and the proximity of the solutions before and after a deformation in the proposed method. The obtained relation provides guidance on how to deform the continuation parameter. The effectiveness of this method is confirmed through numerical examples

Passivity-Based Lag-Compensators with Input Saturation for Mechanical Port-Hamiltonian Systems without Velocity Measurements

In this work, we propose a passivity-based control technique, where the resulting controllers can be interpreted as lag-compensators for nonlinear mechanical systems described in the port-Hamiltonian framework. The proposed methodology considers a dynamic controller such that the relationship between the control input and the error signal of interest can be expressed in terms of a transfer function. Accordingly, the control gains can be tuned through a frequency analysis approach. Additionally, two practical advantages of the resulting controllers are that they do not require velocity measurements, and they can cope with input saturation. We illustrate the applicability of the proposed methodology through the stabilization of a planar manipulator, where the experimental results corroborate the effectiveness of the technique

On Passivity-Based High-Order Compensators for Mechanical Port-Hamiltonian Systems without Velocity Measurements

In this work, we propose passivity-based control techniques, where the resulting controllers include the entire class of dynamic output feedback controllers that preserve the port-Hamiltonian structure. The proposed methodology considers a dynamic output feedback controller such that the linearized relationship between the control inputs and the outputs of interest can be interpreted as a high-order compensator. Accordingly, the controllers are studied in the framework of the transfer functions, and the control gains can be tuned through a frequency analysis approach while ensuring the stability of the closed-loop system. Additionally, the controllers have the advantage that they do not require velocity measurements. We illustrate the applicability of the proposed methodology through a numerical example

Passivity-Based Lag-Compensators with Input Saturation for Mechanical Port-Hamiltonian Systems Without Velocity Measurements

In this work, we propose a passivity-based control technique, where the resulting controllers can be interpreted as lag-compensators for nonlinear mechanical systems described in the port-Hamiltonian framework. The proposed methodology considers a dynamic controller such that the relationship between the control input and the error signal of interest can be expressed in terms of a transfer function. Accordingly, the control gains can be tuned through a frequency analysis approach. Additionally, two practical advantages of the resulting controllers are that they do not require velocity measurements, and they can cope with input saturation. We illustrate the applicability of the proposed methodology through the stabilization of a planar manipulator, where the experimental results corroborate the effectiveness of the technique

Identification of Multiple-Mode Linear Models Based on Particle Swarm Optimizer with Cyclic Network Mechanism

This paper studies the metaheuristic optimizer-based direct identification of a multiple-mode system consisting of a finite set of linear regression representations of subsystems. To this end, the concept of a multiple-mode linear regression model is first introduced, and its identification issues are established. A method for reducing the identification problem for multiple-mode models to an optimization problem is also described in detail. Then, to overcome the difficulties that arise because the formulated optimization problem is inherently ill-conditioned and nonconvex, the cyclic-network-topology-based constrained particle swarm optimizer (CNT-CPSO) is introduced, and a concrete procedure for the CNT-CPSO-based identification methodology is developed. This scheme requires no prior knowledge of the mode transitions between subsystems and, unlike some conventional methods, can handle a large amount of data without difficulty during the identification process. This is one of the distinguishing features of the proposed method. The paper also considers an extension of the CNT-CPSO-based identification scheme that makes it possible to simultaneously obtain both the optimal parameters of the multiple submodels and a certain decision parameter involved in the mode transition criteria. Finally, an experimental setup using a DC motor system is established to demonstrate the practical usability of the proposed metaheuristic optimizer-based identification scheme for developing a multiple-mode linear regression model

連続時間モデル同定に関する研究

京都大学0048新制・課程博士博士(情報学)甲第16218号情博第423号新制||情||77(附属図書館)28797京都大学大学院情報学研究科システム科学専攻(主査)教授 杉江 俊治, 教授 酒井 英昭, 教授 太田 快人学位規則第4条第1項該当Doctor of InformaticsKyoto UniversityDA

A Study on Numerical Solutions of Hamilton-Jacobi-Bellman Equations Based on Successive Approximation Approach

This paper presents a numerical approach to solve the Hamilton-Jacobi-Bellman (HJB) equation, which arises in nonlinear optimal control. In this approach, we first use the successive approximation to reduce the HJB equation, a nonlinear partial differential equation (PDE), to a sequence of linear PDEs called a generalized-Hamilton-Jacobi-Bellman (GHJB) equation. Secondly, the solution of the GHJB equation is decomposed by basis functions whose coefficients are obtained by the collocation method. This step is conducted by solving quadratic programming under the constraints which reflect the conditions that the value function must satisfy. This approach enables us to obtain a stabilizing solution of problems with strong nonlinearity. The application to swing up and stabilization control of an inverted pendulum illustrates the effectiveness of the proposed approach