arXiv subjects

Toshiyuki Ohtsuka

Publications and source records attributed to Toshiyuki Ohtsuka.

23 records · Page 2Linked to original sources

arXiv2022

Bayesian filtering for nonlinear stochastic systems using holonomic gradient method with integral transform

This paper proposes a symbolic-numeric Bayesian filtering method for a class of discrete-time nonlinear stochastic systems to achieve high accuracy with a relatively small online computational cost. The proposed method is based on the holonomic gradient method (HGM), which is a symbolic-numeric method to evaluate integrals efficiently depending on several parameters. By approximating the posterior probability density function (PDF) of the state as a Gaussian PDF, the update process of its mean and variance can be formulated as evaluations of several integrals that exactly take into account the nonlinearity of the system dynamics. An integral transform is used to evaluate these integrals more efficiently using the HGM than our previous method. Further, a numerical example is provided to demonstrate the efficiency of the proposed method compared to other existing methods.

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arXiv2021

Structure-Exploiting Newton-Type Method for Optimal Control of Switched Systems

This study proposes an efficient Newton-type method for the optimal control of switched systems under a given mode sequence. A mesh-refinement-based approach is utilized to discretize continuous-time optimal control problems (OCPs) and formulate a nonlinear program (NLP), which guarantees the local convergence of a Newton-type method. A dedicated structure-exploiting algorithm (Riccati recursion) is proposed to perform a Newton-type method for the NLP efficiently because its sparsity structure is different from a standard OCP. The proposed method computes each Newton step with linear time-complexity for the total number of discretization grids as the standard Riccati recursion algorithm. Additionally, the computation is always successful if the solution is sufficiently close to a local minimum. Conversely, general quadratic programming (QP) solvers cannot accomplish this because the Hessian matrix is inherently indefinite. Moreover, a modification on the reduced Hessian matrix is proposed using the nature of the Riccati recursion algorithm as the dynamic programming for a QP subproblem to enhance the convergence. A numerical comparison is conducted with off-the-shelf NLP solvers, which demonstrates that the proposed method is up to two orders of magnitude faster. Whole-body optimal control of quadrupedal gaits is also demonstrated and shows that the proposed method can achieve the whole-body model predictive control (MPC) of robotic systems with rigid contacts.

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arXiv2021

Riccati Recursion for Optimal Control Problems of Nonlinear Switched Systems

We propose an efficient algorithm for the optimal control problems (OCPs) of nonlinear switched systems that optimizes the control input and switching instants simultaneously for a given switching sequence. We consider the switching instants as the optimization variables and formulate the OCP based on the direct multiple shooting method. We derive a linear equation to be solved in Newton's method and propose a Riccati recursion algorithm to solve the linear equation efficiently. The computational time of the proposed method scales linearly with respect to the number of time stages of the horizon as the standard Riccati recursion. Numerical experiments show that the proposed method converges with a significantly shorter computational time than the conventional methods.

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arXiv2020

A Double-Layer Jacobi Method for PDE-Constrained Nonlinear Model Predictive Control

This paper presents a real-time optimization method for nonlinear model predictive control (NMPC) of systems governed by partial differential equations (PDEs). The NMPC problem to be solved is formulated by discretizing the PDE system in space and time by using the finite difference method. The proposed method is called the double-layer Jacobi method, which exploits both the spatial and temporal sparsities of the PDE-constrained NMPC problem. In the upper layer, the NMPC problem is solved by ignoring the temporal couplings of either the state or costate (Lagrange multiplier corresponding to the state equation) equations so that the spatial sparsity is preserved. The lower-layer Jacobi method is a linear solver dedicated to PDE-constrained NMPC problems by exploiting the spatial sparsity. Convergence analysis indicates that the convergence of the proposed method is related to the prediction horizon and regularization. Results of a numerical experiment of controlling a heat transfer process show that the proposed method is two orders of magnitude faster than the conventional structure-exploiting Newton's method.

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arXiv2016

Nonlinear Eigenvalue Approach to Differential Riccati Equations for Contraction Analysis

In this paper, we extend the eigenvalue method of the algebraic Riccati equation to the differential Riccati equation (DRE) in contraction analysis. One of the main results is showing that solutions to the DRE can be expressed as functions of nonlinear eigenvectors of the differential Hamiltonian matrix. Moreover, under an assumption for the differential Hamiltonian matrix, real symmetricity, regularity, and positive semidefiniteness of solutions are characterized by nonlinear eigenvalues and eigenvectors.

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