arXiv subjects

Yuji Ito

Publications and source records attributed to Yuji Ito.

At least 19 recordsLinked to original sources

arXiv2026

Avoiding Semi-Infinite Programming in Distributionally Robust Control Based on Mean-Variance Metrics

Conventional stochastic control methods have several limitations. They focus on optimizing the average performance and, in some cases, performance variability; however, their problem settings still require an explicit specification of the probability distributions that determine the system's stochastic behavior. Distributionally robust control (DRC) methods have recently been developed to address these challenges. However, many DRC approaches involve handling infinitely many inequalities. For instance, DRC problems based on the Wasserstein distance are commonly obtained by solving semi-infinite programming (SIP) problems. Our proposed method eliminates the need for SIP when solving discrete-time, discounted, distributionally robust optimal control problems. By introducing a penalty term based on a specific distributional distance, we establish upper bounds, and under appropriate conditions, demonstrate the equivalence between distributionally robust optimization problems and mean-variance minimization problems. This reformulation reduces the original DRC problem to a discounted mean-variance cost optimization problem. In linear-quadratic regulator settings, the corresponding control laws are obtained by solving the Riccati equation. Numerical experiments demonstrate that the theoretical maximum value of the discounted cumulative cost for the proposed method is lower than that for the conventional method.

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arXiv2025

Explicit Reformulation of Discrete Distributionally Robust Optimization Problems

Distributionally robust optimization (DRO) is an effective framework for controlling real-world systems with various uncertainties, typically modeled using distributional uncertainty balls. However, DRO problems often involve infinitely many inequality constraints, rendering exact solutions computationally expensive. In this study, we propose a discrete DRO (DDRO) method that significantly simplifies the problem by reducing it to a single trivial constraint. Specifically, the proposed method utilizes two types of distributional uncertainty balls to reformulate the DDRO problem into a single-layer smooth convex program, significantly improving tractability. Furthermore, we provide practical guidance for selecting the appropriate ball sizes. The original DDRO problem is further reformulated into two optimization problems: one minimizing the mean and standard deviation, and the other minimizing the conditional value at risk (CVaR). These formulations account for the choice of ball sizes, thereby enhancing the practical applicability of the method. The proposed method was applied to a distributionally robust patrol-agent design problem, identifying a Pareto front in which the mean and standard deviation of the mean hitting time varied by up to 3% and 14%, respectively, while achieving a CVaR reduction of up to 13%.

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arXiv2025

Reservoir Predictive Path Integral Control for Unknown Nonlinear Dynamics

Neural networks have found extensive application in data-driven control of nonlinear dynamical systems, yet fast online identification and control of unknown dynamics remain central challenges. To meet these challenges, this paper integrates echo-state networks (ESNs)--reservoir computing models implemented with recurrent neural networks--and model predictive path integral (MPPI) control--sampling-based variants of model predictive control. The proposed reservoir predictive path integral (RPPI) enables fast learning of nonlinear dynamics with ESNs and exploits the learned nonlinearities directly in MPPI control computation without linearization approximations. This framework is further extended to uncertainty-aware RPPI (URPPI), which achieves robust stochastic control by treating ESN output weights as random variables and minimizing an expected cost over their distribution to account for identification errors. Experiments on controlling a Duffing oscillator and a four-tank system demonstrate that URPPI improves control performance, reducing control costs by up to 60% compared to traditional quadratic programming-based model predictive control methods.

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arXiv2025

Probability-Raising Causality for Uncertain Parametric Markov Decision Processes with PAC Guarantees

Recent decision-making systems are increasingly complicated, making it crucial to verify and understand their behavior for a given specification. A promising approach is to comprehensively explain undesired behavior in the systems modeled by Markov decision processes (MDPs) through formal verification and causal reasoning. However, the reliable explanation using model-based probabilistic causal analysis has not been explored when the MDP's transition probabilities are uncertain. This paper proposes a method to identify potential causes of undesired behaviors in an uncertain parametric MDP (upMDP) using parameter sampling, model checking, and a set covering for the samples. A cause is defined as a subset of states based on a probability-raising principle. We show that the probability of each identified subset being a cause exceeds a specified threshold. Further, a lower bound of the probability that the undesired paths visit the subsets is maximized as much as possible while satisfying a nonredundancy condition. While computing these probabilities is complicated, this study derives probabilistically approximately correct lower bounds of both probabilities by the sampling. We demonstrate the effectiveness of the proposed method through a path-planning scenario.

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arXiv2025

Stabilizing Optimal Control for Nonlinear Stochastic Systems: A Parametric Gradient-Based Approach

This study proposes a method for designing stabilizing suboptimal controllers for nonlinear stochastic systems. These systems include time-invariant stochastic parameters that represent uncertainty of dynamics, posing two key difficulties in optimal control. Firstly, the time-invariant stochastic nature violates the principle of optimality and Hamilton-Jacobi equations, which are fundamental tools for solving optimal control problems. Secondly, nonlinear systems must be robustly stabilized against these stochastic parameters. To overcome these difficulties simultaneously, this study presents a parametric-gradient-based method with a penalty function. A controller and cost function are parameterized using basis functions, and a gradient method is employed to optimize the controller by minimizing the parameterized cost function. Crucial challenges in this approach are parameterizing the cost function appropriately and deriving the gradient of the cost. This study provides explicit formulations of an optimally parameterized cost and its gradient. Furthermore, a suitable penalty function is proposed to ensure robust stability, even when using the gradient method. Consequently, the gradient method produces a suboptimal feedback controller that guarantees the robust stability. The effectiveness of the proposed method is demonstrated through numerical simulations, highlighting its performance in comparison with other baseline methods.

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arXiv2024

Discrete Distributionally Robust Optimal Control with Explicitly Constrained Optimization

Distributionally robust optimal control (DROC) is gaining interest. This study presents a reformulation method for discrete DROC (DDROC) problems to design optimal control policies under a worst-case distributional uncertainty. The reformulation of DDROC problems impacts both the utility of tractable improvements in continuous DROC problems and the inherent discretization modeling of DROC problems. DROC is believed to have tractability issues; namely, infinite inequalities emerge over the distribution space. Therefore, investigating tractable reformulation methods for these DROC problems is crucial. One such method utilizes the strong dualities of the worst-case expectations. However, previous studies demonstrated that certain non-trivial inequalities remain after the reformulation. To enhance the tractability of DDROC, the proposed method reformulates DDROC problems into one-layer smooth convex programming with only a few trivial inequalities. The proposed method is applied to a DDROC version of a patrol-agent design problem.

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arXiv2024

Theoretical Analysis of Heteroscedastic Gaussian Processes with Posterior Distributions

This study introduces a novel theoretical framework for analyzing heteroscedastic Gaussian processes (HGPs) that identify unknown systems in a data-driven manner. Although HGPs effectively address the heteroscedasticity of noise in complex training datasets, calculating the exact posterior distributions of the HGPs is challenging, as these distributions are no longer multivariate normal. This study derives the exact means, variances, and cumulative distributions of the posterior distributions. Furthermore, the derived theoretical findings are applied to a chance-constrained tracking controller. After an HGP identifies an unknown disturbance in a plant system, the controller can handle chance constraints regarding the system despite the presence of the disturbance.

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arXiv2024

Contraction Analysis of Continuation Method for Suboptimal Model Predictive Control

This letter analyzes the contraction property of the nonlinear systems controlled by suboptimal model predictive control (MPC) using the continuation method. We propose a contraction metric that reflects the hierarchical dynamics inherent in the continuation method. We derive a pair of matrix inequalities that elucidate the impact of suboptimality on the contraction of the optimally controlled closed-loop system. A numerical example is presented to verify our contraction analysis. Our results are applicable to other MPCs than stabilization, including economic MPC.

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arXiv2024

Dirichlet Logistic Gaussian Processes for Evaluation of Black-Box Stochastic Systems under Complex Requirements

The requirement-driven performance evaluation of a black-box cyber-physical system (CPS) that utilizes machine learning methods has proven to be an effective way to assess the quality of the CPS. However, the distributional evaluation of the performance has been poorly considered. Although many uncertainty estimation methods have been advocated, they have not successfully estimated highly complex performance distributions under small data. In this paper, we propose a method to distributionally evaluate the performance under complex requirements using small input-trajectory data. To handle the unknown complex probability distributions under small data, we discretize the corresponding performance measure, yielding a discrete random process over an input region. Then, we propose a semiparametric Bayesian model of the discrete process based on a Dirichlet random field whose parameter function is represented by multiple logistic Gaussian processes (LGPs). The Dirichlet posterior parameter function is estimated through the LGP posteriors in a reasonable and conservative fashion. We show that the proposed Bayesian model converges to the true discrete random process as the number of data becomes large enough. We also empirically demonstrate the effectiveness of the proposed method by simulation.

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arXiv2024

An Uncertainty-aware, Mesh-free Numerical Method for Kolmogorov PDEs

This study introduces an uncertainty-aware, mesh-free numerical method for solving Kolmogorov PDEs. In the proposed method, we use Gaussian process regression (GPR) to smoothly interpolate pointwise solutions that are obtained by Monte Carlo methods based on the Feynman-Kac formula. The proposed method has two main advantages: 1. uncertainty assessment, which is facilitated by the probabilistic nature of GPR, and 2. mesh-free computation, which allows efficient handling of high-dimensional PDEs. The quality of the solution is improved by adjusting the kernel function and incorporating noise information from the Monte Carlo samples into the GPR noise model. The performance of the method is rigorously analyzed based on a theoretical lower bound on the posterior variance, which serves as a measure of the error between the numerical and true solutions. Extensive tests on three representative PDEs demonstrate the high accuracy and robustness of the method compared to existing methods.

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arXiv2023

Weighted Stochastic Riccati Equations for Generalization of Linear Optimal Control

This paper presents weighted stochastic Riccati (WSR) equations for designing multiple types of optimal controllers for linear stochastic systems. The stochastic system matrices are independent and identically distributed (i.i.d.) to represent uncertainty and noise in the systems. However, it is difficult to design multiple types of controllers for systems with i.i.d. matrices while the stochasticity can invoke unpredictable control results. A critical limitation of such i.i.d. systems is that Riccati-like algebraic equations cannot be applied to complex controller design. To overcome this limitation, the proposed WSR equations employ a weighted expectation of stochastic algebraic equations. The weighted expectation is calculated using a weight function designed to handle statistical properties of the control policy. Solutions to the WSR equations provide multiple policies depending on the weight function, which contain the deterministic optimal, stochastic optimal, and risk-sensitive linear (RSL) control. This study presents two approaches to solve the WSR equations efficiently: calculating WSR difference equations iteratively and employing Newton's method. Moreover, designing the weight function yields a novel controller termed the robust RSL controller that has both a risk-sensitive policy and robustness to randomness occurring in stochastic control design.

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arXiv2023

Convergence Analysis of the Upwind Difference Methods for Hamilton-Jacobi-Bellman Equations

This paper investigates the convergence properties of the upwind difference scheme for the Hamilton--Jacobi--Bellman (HJB) equation, a central partial differential equation in optimal control theory. First, assuming the existence of a classical solution, we show that the numerical solution converges to the true solution with a first-order rate with respect to the time step. This result complements the square-root rate established in previous studies for viscosity solutions. Second, by exploiting the correspondence between HJB equations and conservation laws, we prove the convergence of the optimal control input. This analysis is crucial for practical applications where the control input is the primary quantity of interest, yet it has rarely been addressed in previous studies. Finally, we confirm the validity of our theoretical results through numerical experiments on typical control problems.

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arXiv2022

Second Moment Polytopic Systems: Generalization of Uncertain Stochastic Linear Dynamics

This paper presents a new paradigm to stabilize uncertain stochastic linear systems. Herein, second moment polytopic (SMP) systems are proposed that generalize systems with both uncertainty and randomness. The SMP systems are characterized by second moments of the stochastic system matrices and the uncertain parameters. Further, a fundamental theory for guaranteeing stability of the SMP systems is established. It is challenging to analyze the SMP systems owing to both the uncertainty and randomness. An idea to overcome this difficulty is to expand the SMP systems and exclude the randomness. Because the expanded systems contain only the uncertainty, their stability can be analyzed via robust stability theory. The stability of the expanded systems is equivalent to statistical stability of the SMP systems. These facts provide sufficient conditions for the stability of the SMP systems as linear matrix inequalities (MIs). In controller design for the SMP systems, the linear MIs reduce to cubic MIs whose solutions correspond to feedback gains. The cubic MIs are transformed into simpler quadratic MIs that can be solved using optimization techniques. Moreover, solving such non-convex MIs is relaxed into the iteration of a convex optimization. Solutions to the iterative optimization provide feedback gains that stabilize the SMP systems. As demonstrated here, the SMP systems represent linear dynamics with uncertain mean and covariance and other existing systems such as independently identically distributed dynamics and random polytopes. Finally, a numerical simulation shows the effectiveness of the proposed method.

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arXiv2022

A fictitious-play finite-difference method for linearly solvable mean field games

An iterative finite difference scheme for mean field games (MFGs) is proposed. The target MFGs are derived from control problems for multidimensional systems with advection terms. For such MFGs, linearization using the Cole-Hopf transformation and iterative computation using fictitious play are introduced. This leads to an implementation-friendly algorithm that iteratively solves explicit schemes. The convergence properties of the proposed scheme are mathematically proved by tracking the error of the variable through iterations. Numerical calculations show that the proposed method works stably for both one- and two-dimensional control problems.

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arXiv2020

Optimal Transport-based Coverage Control for Swarm Robot Systems: Generalization of the Voronoi Tessellation-based Method

Swarm robot systems, which consist of many cooperating mobile robots, have attracted attention for their environmental adaptability and fault tolerance advantages. One of the most important tasks for such systems is coverage control, in which robots autonomously deploy to approximate a given spatial distribution. In this study, we formulate a coverage control paradigm using the concept of optimal transport and propose a novel control technique, which we have termed the optimal transport-based coverage control (OTCC) method. The proposed OTCC, derived via the gradient flow of the cost function in the Kantorovich dual problem, is shown to covers a widely used existing control method as a special case. We also perform a Lyapunov stability analysis of the controlled system, and provide numerical calculations to show that the OTCC reproduces target distributions with better performance than the existing control method.

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arXiv2020

Model Predictive Mean Field Games for Controlling Multi-Agent Systems

When controlling multi-agent systems, the trade-off between performance and scalability is a major challenge. Here, we address this difficulty by using mean field games (MFGs), which is a framework that deduces the macroscopic dynamics describing the density profile of agents from their microscopic dynamics. To effectively use the MFG, we propose a model predictive MFG (MP-MFG), which estimates the agent population density profile with using kernel density estimation and manages the input generation with model predictive control. The proposed MP-MFG generates control inputs by monitoring the agent population at each time step, and thus achieves higher robustness than the conventional MFG. Numerical results show that the MP-MFG outperforms the MFG when the agent model has modeling errors or the number of agents in the system is small.

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arXiv2019

Simple Design on Nanoscale Receivers Using CNT Cantilevers

A nanoscale receiver utilizing the cantilever of a carbon nanotube has been developed to detect phase information included in transmitted signals. The existing receiver consists of a phase detector and demodulator which employ a reference wave and carrier signal, respectively. This paper presents a design method to simplify the receiver in structure with enhancing the performance for the phase detection. The reference wave or carrier signal is not needed in the receiver via the proposed design method.

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arXiv2018

Pseudo-perturbation-based Broadcast Control of Multi-agent Systems

The present paper proposes a novel broadcast control (BC) law for multi-agent coordination. A BC framework has been developed to achieve global coordination tasks with low communication volume. The BC law uses broadcast communication, which transmits an identical signal to all agents indiscriminately without any agent-to-agent communication. Unfortunately, all of the agents are required to take numerous random actions because the BC law is based on stochastic optimization. Such random actions degrade the control performance for coordination tasks and may invoke dangerous situations. In order to overcome these drawbacks, the present paper proposes the pseudo-perturbation-based broadcast control (PBC) law, which introduces multiple virtual random actions instead of the single physical action of the BC law. The following advantages of the PBC law are theoretically proven. The PBC law achieves coordination tasks asymptotically with probability 1. Compared with the BC law, unavailing actions are reduced and agents' states converge at least twice as fast. Increasing the number of multiple actions further improves the control performance because averaging multiple actions reduces unavailing randomness. Numerical simulations demonstrate that the PBC improves the control performance as compared with the BC law.

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