In this paper, we investigate the concept of input redundancy of switched systems, where the switching signal is the control input. An input redundant system in this context describes a system in which the same output trajectory can be generated by non-equivalent switching signals. The concept of equivalence in switching signals means that two signals generate identical state trajectories under identical initial conditions. Unlike the linear time-invariant case where input redundancy is uniform in the initial condition, this property is absent in the considered study. For autonomous switched linear systems, we developed a strategy to verify the existence of initial conditions where non-equivalent switching signals produce the same output. A numerical example is presented to illustrate the proposed strategy, for which we also compute the entire set of initial conditions that lead to input redundancy.

Constrained Markov Decision Processes (CMDPs) are widely used for online decision-making under constraints. However, their applicability is often limited by the reliance on expectation-based linear constraints. Chance-Constrained MDPs (CCMDPs) address this by incorporating nonlinear, probabilistic constraints, yet are often intractable and approximated via CVaR-based reformulations. In this letter, we propose a tractable framework for CCMDPs to exactly solve the best deterministic policies based on a three-stage, model-based constraint learning algorithm. Theoretically, we establish a polynomial sample complexity guarantee for feasible policy optimization using a novel distributional concentration analysis. A case study on a thermostatically controlled load demonstrates the effectiveness of our approach.

This paper proposes an active fault diagnosis method for spacecraft attitude control systems with disturbances by utilizing the unknown input observer. Firstly, the spacecraft attitude control system is formulated as a linear time-invariant model under diverse faulty conditions. A general unknown input observer framework is constructed to decouple process disturbances by designing optimal gain matrices, which are analytically obtained by solving an unconstrained optimization problem. Then, zonotopes are utilized to characterize the dynamics of state estimation error, and a set-theoretic unknown input observer is built. To achieve the guaranteed active fault diagnosis, a quadratic program and a mixed-integer quadratic optimization program are formulated to obtain the separating input that can maximize the separation degree of all zonotopes under fault isolation and input saturation constraints. Finally, an illustrative example is provided to verify the effectiveness of the proposed active fault diagnosis method.

This letter presents a novel anti-windup adaptive PID controller for trajectory tracking in input-constrained DC-DC buck converters supplying resistive and current loads under parametric uncertainty. The proposed control scheme extends the classical PID architecture by incorporating nonlinear integral action, an adaptive law for online parameter estimation, and a back-calculation-based anti-windup mechanism to address actuator saturation. A Lyapunov-based design framework is employed to establish global asymptotic stability, even in the presence of time-varying references and saturation constraints. Notably, anti-windup strategies grounded in Lyapunov theory for time-varying nonlinear systems are seldom available, making this contribution a significant advancement. Experimental validation on a laboratory buck converter confirms improved tracking accuracy and transient performance compared to conventional PID control, particularly under aggressive parameter variations and saturation-induced nonlinearities.

We study noncooperative games with uncertain payoffs, where agents display irrational behaviors in response to underlying risk factors. Our formulation incorporates prospect theory, a behavioral model used to describe agents’ risk attitude, into the equilibrium theory of noncooperative <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N-$ </tex-math></inline-formula>agent games. We show that the resulting nonconvex nonsmooth game admits equilibria and provide convergence guarantees for their computation. Further, the concept of “Price of Irrationality” is introduced to quantify the suboptimality induced by irrational behaviors. Finally, we provide bounds on the performance of a class of prospect theoretic aggregative games and illustrate our results on an electricity market game.

The discrete empirical interpolation method (DEIM) is a widely used masked projection technique to efficiently approximate nonlinear functions in the model reduction of nonlinear dynamical systems. There exist many upper bounds on the error between the nonlinear function and its masked projection. However, they overestimate the error, especially in the case of many sample points. In this paper, we have improved a posteriori, heuristic, and a priori error bounds on the DEIM and related masked projection methods for the case of many sample points. The proposed bounds are shown, both theoretically and numerically, to be tighter than the existing state-of-the-art bounds in the literature.

This paper presents a distributed framework for simultaneous rigid formation control and trajectory tracking in n dimensional space (n=2,3), motivated by coordinated multi-agent transport, cooperative surveillance, and fractionated spacecraft applications, which demand flexible and scalable alternatives to traditional single-agent approaches. In scenarios where only one agent knows its own global position, and each agent measures only the relative positions of its neighbors, the proposed framework integrates a two-layer decentralized estimator with distributed centroid tracking, orientation alignment, and formation maintenance controllers. The first estimator layer employs a consensus-based self-estimation law, ensuring exponential convergence to actual value. The second estimator layer extends this capability, allowing agents to estimate the positions of their peers, and hence cooperatively compute the formation centroid and orientation. Tracking of predefined formation centroid and orientation trajectories is achieved via three distributed control laws: one for formation maintenance, one for centroid trajectory tracking, and one for aligning the formation orientation, using unit complex numbers in 2D and unit quaternions in 3D. Lyapunov-based analysis establishes exponential convergence for all estimation and control components. Simulations demonstrate the formation’s ability to maintain geometric integrity, track trajectories, and achieve desired orientations, all within a distributed framework.

We present a GPU-accelerated proximal message passing algorithm for large-scale network utility maximization (NUM). NUM is a fundamental problem in resource allocation, where resources are allocated across various streams in a network to maximize total utility while respecting link capacity constraints. Our method, a variant of ADMM, requires only sparse matrix–vector multiplies with the link–route matrix and element-wise proximal operator evaluations, enabling fully parallel updates across streams and links. It also supports heterogeneous utility types, including logarithmic utilities common in NUM, and does not assume strict concavity. We implement our method in PyTorch and demonstrate its performance on problems with tens of millions of variables and constraints, achieving 4× to 20× speedups over existing CPU and GPU solvers and solving problem sizes that exhaust the memory of baseline methods. Additionally, our algorithm is robust to congestion and capacity degradation. A time-expanded transit seat allocation case study illustrates how our approach yields interpretable allocations in realistic networks.

This letter proposes a novel prescribed performance time delay control (PTDC) strategy for trajectory tracking in robot manipulators with uncertain dynamics. By integrating prescribed performance control (PPC) into the time delay control (TDC) framework, the proposed PTDC ensures prescribed performance, featuring bounded transient behavior with low overshoot and improved steady-state accuracy, without requiring detailed knowledge of system dynamics. The control algorithm features a simple structure, low computational overhead, and easy deployment on real-time robotic platforms. Lyapunov’s stability theory and Barbalat’s lemma are applied to rigorously prove global asymptotic stability and prescribed performance guarantees. Both simulations and SCARA robot experiments demonstrate that PTDC significantly outperforms existing TDC schemes in position tracking accuracy and transient performance.

Differential games featuring multiple weak pursuers against a highly maneuverable evader are critical in aerospace applications, yet remain inherently complex and challenging. In this study, we examine a scenario involving two cooperative weak pursuers and a superior evader, with all participants modeled by inertial dynamics during high-speed encounters. We derive the value function using reachable sets and accordingly propose an open-loop Stackelberg state-feedback strategy. Furthermore, we demonstrate that this strategy constitutes a Nash equilibrium in the closed-loop game over the entire state space by showing that the pursuers’ strategy guarantees that the payoff function is less than or equal to the value function, while the evader’s strategy guarantees that payoff function is greater than or equal to the value function. Simulation results are provided, which corroborate our theoretical analysis.