インサイト - Optimal Control

### Overtaking Optimal Control for Linear Time-Invariant Systems with Unknown Disturbances: A Near-Optimal Approach

This paper proposes a novel near-optimal control strategy for linear time-invariant systems subject to unknown disturbances, aiming to achieve both optimal steady-state performance and improved transient performance characterized by overtaking optimality.

### Optimal Control of Fractional Punishment in Optional Public Goods Game to Promote Cooperation

Optimal control can be used to adaptively apply fractional punishment in optional public goods games to promote cooperation at a lower cost compared to constant punishment strategies.

### Quantifying the Safety of Trajectories by Minimizing the Peak Control Effort Required to Crash into an Unsafe Set

The core message of this article is that the safety of trajectories of a dynamical system can be quantified by the minimum control effort (perturbation intensity) required to render the system unsafe and cause it to crash into an unsafe set.

### Optimal Control of a First-Order System with Global Aftereffect on Quantum Graphs

The core message of this article is to extend the problem of damping a first-order control system with aftereffect, previously considered only on an interval, to an arbitrary tree graph. The authors establish the equivalence of the corresponding variational problem to a self-adjoint boundary value problem on the tree, and prove the unique solvability of both problems.

### Optimality Conditions and Regularity Properties in Infinite-Dimensional Optimal Control Problems

The core message of this article is to present a survey on the properties of Strong Metric Regularity (SMR) and Strong Metric subRegularity (SMsR) of mappings representing first order optimality conditions (optimality mappings) in infinite dimensional spaces, with a focus on optimal control problems for ODE systems or PDEs. The authors emphasize an extension of these concepts involving two metrics either in the domain or in the image spaces, and show the relevance of this extension in optimal control.

### 무한 시간 혼합 H2/H∞ 제어의 최적 해법

이 논문에서는 무한 시간 혼합 H2/H∞ 제어 문제에 대한 정확한 폐루프 해법을 제시한다. 최적 제어기는 비합리적이지만, 유한 차원 매개변수로 완전히 특성화될 수 있다. 또한 제안된 반복 알고리즘을 통해 최적 제어기를 주파수 영역에서 효율적으로 계산할 수 있다.

### Optimal Infinite-Horizon Mixed H2/H∞ Control for Discrete-Time Linear Systems

The optimal causal controller that minimizes the H2-cost of the closed-loop system subject to an H∞ constraint can be characterized in the frequency domain, even though it is non-rational.

### Optimal Control of Stochastic Reaction Networks with Mass-Action Kinetics

The core message of this paper is to develop an optimal control theory for stochastic reaction networks, which is an important problem with significant implications for the control of biological systems. The authors provide a comprehensive analysis of the continuous-time and sampled-data optimal control problems for stochastic reaction networks, deriving the optimal control laws and characterizing them in terms of Hamilton-Jacobi-Bellman equations and Riccati differential equations.

### Optimal Control of Discrete-Time Systems with Bounded Disturbances

This paper introduces an optimal control approach for linear discrete-time systems subject to bounded disturbances, based on a novel duality between ellipsoidal approximations of reachable and hardly observable sets.

### Optimal Distributionally Robust Control for Linear Quadratic Gaussian Systems under Distributed Uncertainty

The paper proposes a new paradigm for the robustification of the LQG controller against distributional uncertainties on the noise process. The controller optimizes the closed-loop performance in the worst possible scenario under the constraint that the noise distributional aberrance does not exceed a certain threshold limiting the relative entropy between the actual noise distribution and the nominal one. The key novelty is that the bounds on the distributional aberrance can be arbitrarily distributed along the whole disturbance trajectory.