Optimal control of inter-population disease spread via reaction-diffusion models.

Indefinite mean-field linear–quadratic optimal control problem with partial information

Forecasting and optimal control model to assess the potential role of vaccine hesitancy and supportive care in East Java measles outbreak.

In this article, we investigate the problem of adaptive safe critic control design for stochastic multiagent systems (MASs) subject to asymmetric state and input constraints. To systematically address asymmetric state constraints, a unified transformation function (UTF) is proposed to convert the constrained consensus control problem into the stability analysis of an unconstrained error system. In addition, a nonquadratic cost function is incorporated to address input limitations effectively. Building upon these developments, a time-varying Hamilton-Jacobi-Bellman equation (HJBE) is formulated by integrating the Bellman optimality principle with Itô's lemma, thereby accommodating stochastic disturbances and enhancing controller robustness. To improve data utilization and eliminate reliance on explicit drift dynamics, an integral reinforcement learning (IRL) algorithm is developed within this framework. Furthermore, a time-varying single-critic network is designed to approximate the solution to the HJBE and generate optimal control policies, thereby considerably reducing computational complexity. To further enhance learning efficiency and relax the persistent excitation (PE) condition, the experience replay (ER) technique is incorporated into the update process of the critic weight. Finally, two simulation examples are provided to verify the feasibility and effectiveness of the proposed approach.

By means of a fully actuated system (FAS) approach, this article is concerned with an anti-disturbance tracking control problem toward a class of lumped disturbances containing the model uncertainties and external disturbances. A FAS predictive control with a generalized proportional-integral observer (GPIO) is presented to address this problem. Concretely, a FAS model of discrete-time nonlinear systems with the lumped disturbances is firstly given as a control-oriented one. Then, a GPIO is developed to achieve an accurate estimation for the lumped disturbances by adopting a less conservative disturbance assumption, which provides a better foundation to construct a disturbance preview. Furthermore, an incremental FAS (IFAS) prediction model with a disturbance preview is constructed by utilizing a new type of Diophantine Equation. Dependent on this IFAS prediction model, the multistep ahead predictions can be obtained to minimize an objective function to yield an optimal anti-disturbance controller, such that the desired tracking performance can be guaranteed. The depth analysis derives a sufficient condition for the bounded stability and tracking performance of the closed-loop FASs. The proposed GPIO-based FAS predictive control provides a solution to the spacecraft attitude control for verifying the feasibility.

Observer-based prescribed-time optimal neural consensus control for six-rotor UAVs: A novel actor-critic reinforcement learning strategy.

In complex real-world traffic environments, ramp merging tasks pose significant challenges for platoon control systems. Conventional control methods often lack the flexibility required for coordinated platoon merging scenarios and fail to adequately address inter-vehicle safety constraints. Consequently, developing control strategies that satisfy safety constraints while ensuring precise merging coordination becomes imperative. This paper proposes a platoon safety-oriented merging control scheme for autonomous vehicles (AVs) within an optimal control framework. First, we systematically investigate the definition and selection methodology of merging strategies in platoon merging scenarios. Leveraging this approach, a platoon merging performance function is formulated, with merging sequences determined through comparative evaluation of strategy-specific performance metrics. Subsequently, the safety constraints and terminal merging conditions are incorporated into the performance index design via optimal control theory, transforming the merging coordination and safety assurance tasks into an optimal control problem. Finally, simulation results validate the proposed tracking control scheme, demonstrating its reliability and effectiveness through comprehensive performance analysis.

Specialized or General-Purpose-The Wrong Question for Mental Health AI Safety.

This paper is concerned with the sideways problem for parabolic equations in a bounded domain. The Dirichlet data on the remaining part of the boundary is reconstructed from the Dirichlet and Neumann measurements on a portion of the boundary. Based on existing theories, the uniqueness of the inverse problem can be established, and its ill-posedness is analyzed. Then, by introducing two auxiliary problems, the inverse problem is reformulated as an optimal control problem with Kohn-Vogelius regularization. We further prove the existence and stability of solutions to the optimal control problem. Finally, a physics-informed neural network framework based on the Kohn-Vogelius type functional is applied to several numerical examples.

Building upon the ODE model describing the dynamics of healthy and leukemic cells introduced in Kumar et al. (2024); Stiehl and Marciniak-Czochra (2012), we propose an extended framework that incorporates a control variable representing the effects of chemotherapy. This extension aims to provide a more refined mathematical basis for investigating anti-cancer strategies. First, we perform a stability analysis of the equilibria associated with healthy and leukemic states, partly estimated from clinical data. This analysis reveals a complex structure, including the emergence of a continuum of coexistence states and bifurcation thresholds that play a key role in the subsequent optimization stage. Based on these findings, we investigate an optimal control problem to minimize leukemia stem cells while limiting drug toxicity. Pontryagin's Maximum Principle provides necessary conditions for optimality, and direct numerical optimization confirms the predicted structures, motivating the study of the static problem. This static formulation reveals an unconventional feature: the cost functional becomes set-valued due to the continuum of equilibria, placing the problem outside the scope of standard methods. Simulations reveal a turnpike phenomenon, where over long time horizons the dynamic trajectories closely approximate the ideal static structure. Finally, a sensitivity analysis of the performance criterion with respect to key parameters complements the study, providing preliminary insights into which biological mechanisms may influence the optimal therapeutic outcomes. We conclude with a discussion of these findings.

This paper investigates the asymptotic tracking control problem for multi-agent systems (MASs) under deception attacks, with unknown nonlinear dynamics and time-varying asymmetric state constraints. First, based on the backstepping control framework, a state-dependent function is introduced, and a new error coordinate transformation is defined to design a distributed controller, eliminating the feasibility condition requirement of virtual controllers in barrier Lyapunov function (BLF)-based methods. Second, an improved first-order nonlinear filter is designed based on the dynamic surface control (DSC) technique, which not only resolves the differential explosion problem caused by virtual controllers in the backstepping control method but also eliminates the adverse effects of unknown terms on the asymptotic stability. It can be proven that under the proposed control strategy, (1) asymptotic convergence of consensus errors is achieved, and (2) the states of MASs satisfy the preset constraints. Finally, simulation results demonstrate the effectiveness of the proposed control scheme.

Abstract This paper studies a computationally efficient and robust method for path planning and path following tasks for unmanned systems. The method is based on relaxed differential-algebraic equations (DAEs), which allow to handle deviations from a prescribed path. The relaxation is designed by a suitably formulated optimal control problem with the aim to guide the system back to the desired path in a smooth way. The approach merely requires to solve a higher index DAE numerically. In addition, a parametric sensitivity analysis can be used to obtain Taylor approximations of perturbed solutions at very low computational cost. We demonstrate the method for a path following task with an unmanned ground vehicle (UGV) and a transition to hover maneuver of an unmanned aerial vehicle (UAV).

Predefined-time affine formation tracking control of unmanned surface vehicles with input saturation via adaptive fuzzy observers.

We propose a mathematical model for the growth and treatment of Undifferentiated Pleomorphic Sarcoma (UPS) using a system of nonlinear differential equations. The model combines Gompertz-type tumor growth with surface-dependent necrotic loss, surgical resection with residual disease, postoperative recovery, tumor-immune interaction, and radiation treatment scheduling. We study the mathematical properties of the model and obtain several results. The growth equation shows the existence of a threshold below which the tumor cannot survive and may disappear. The postoperative phase exhibits an early inflammatory stage followed by proliferative recovery. For the tumor-immune subsystem, equilibrium states and local stability conditions are identified. The radiation treatment problem is formulated as an optimal control problem, and the optimal strategy is shown to be of bang-bang type. The model suggests that tumor recurrence depends not only on tumor growth itself but also on residual disease, postoperative dynamics, immune response, and treatment timing.

This paper addresses the leader-following consensus control problem for a class of nonlinear multi-agent systems(MASs) in the presence of denial of service (DoS) attacks. The primary objectives are threefold: ensuring reliable reception of neighbour information by followers during DoS attacks, constructing a leader observer to provide trackable reference signals for followers, and designing a control strategy to achieve rapid tracking of the observer. To address the communication disruption caused by DoS attacks in the first objective, a multi-channel transmission technique using distributed-try-once-discard (D-TOD) protocol is proposed. Furthermore, a distributed observer utilising neighbour information is designed to achieve effective leader state estimation. A predefined-time sliding surface control strategy is then developed by integrating sliding surface control and backstepping techniques. This ensures the follower's trajectory converges to the leader observer within a predetermined timeframe, and the achievement of the control objective is rigorously proven via Lyapunov function analysis.

This paper establishes a time delay necessary and sufficient stochastic maximum principle for a McKean–Vlasov model with randomness described by Brownian motions and Poisson jumps with noisy observation. The controlled delayed state process is governed by a general McKean–Vlasov nonlinear Itô stochastic differential equation with time delay (MVDSDE) driven by Poisson random jumps with correlate noisy observation. The coefficients of the controlled delay system depend on the state process as well as of its distribution and the control variable with time delay. Our main result is proved by applying convex perturbation method, approximate technique, Girsanov's lemma, and L -partial derivatives with respect to distribution. Finally, some examples with delay partially observed linear quadratic control problem of McKean–Vlasov type with Poisson jumps are studied, where we derive the explicit expression of the optimal control in feedback form.

This article investigates the dual-mode distributed model predictive control (DMPC) problem for multiagent systems (MASs) in the context of noncooperative games. With regard to the mutual influence of neighbor agents, a novel objective function is developed. It consists of three main parts: the conventional quadratic function of MPC accounting for model performance and control cost, the difference between the local agent and its neighbors to guarantee the consensus, and the neighbor's disturbance to obtain the anti-interference capability. To find a nice balance between the online computational burden, practical feasibility, and model performance, a dual-model control strategy is proposed. Then, to handle the couplings resulting from the agents' communication and the negative influence caused by neighbors, the quadratic boundedness lemma, Rayleigh-Ritz theorem, and slack matrix technique are employed, and therefore, both online and offline problems with solvability are readily established. Additionally, sufficient conditions are provided for the guarantee of stability, and an iterative DMPC-based algorithm is designed to ensure that all the agents reach the $\varepsilon $ -Nash equilibrium ( $\varepsilon $ -NE). Finally, a simulation example of a spacecraft system is presented to validate the effectiveness of the proposed dual-mode DMPC, demonstrating that the spacecraft system can converge to the $\varepsilon $ -NE in a distributed manner.

Proteins and lipids of eukaryotes are decorated with glycans: branched chains of sugars that affect their folding, stability, recognition, and therapeutic function. Unlike DNA or proteins that are synthesized from a template, glycans are assembled through enzyme-catalyzed monomer addition reactions as they transit through the compartments of the Golgi apparatus. Thus, glycan production can be viewed as a control problem: the enzyme localization and residence times in compartments must be chosen to produce the desired glycans efficiently. A key complication is the promiscuous nature of enzymes: longer compartment residence times can lead to off-target products even as they allow more complex glycans to be made, creating a trade-off. Here, we formulate glycan synthesis as an abstract chemical kinetic manufacturing problem and ask how enzyme allocations and compartment residence times should be chosen in the presence of this trade-off. We show that nonoverlapping enzyme distributions are optimal for single-glycan manufacture of the trees considered; however, overlapping enzyme distributions attain their maximum yield faster. We then consider simultaneous manufacture of multiple glycans, where optimizing the manufacture of one glycan might reduce the yield of another. Pareto-optimal solutions are a class of solutions that reconcile this trade-off. We explore Pareto-optimal solutions for multiple glycan manufacture and show that small changes in residence times can change the optimal enzyme distribution. Even though overlapping enzyme distributions are suboptimal for all the considered cases of single-glycan manufacture, the Pareto set for multiple glycan manufacture contains overlapping distributions. Together, these results show that Pareto optimality provides a useful framework for interpreting trade-offs in Golgi organization and for controlling glycan outputs in industrial settings such as manufacture of biotherapeutics, many of which are glycosylated.

This paper investigates the load frequency control (LFC) problem of power systems under actuator-side false data injection (FDI) attacks. First, an FDI-aware LFC model is developed to describe corruption in the control input channel. Subsequently, an adaptive event-triggered mechanism (AETM) is introduced to improve communication efficiency, and transmission lag is incorporated into the closed-loop model. Furthermore, a honeypot-gated adaptive compensation mechanism is proposed, where the honeypot detection flag activates the compensation channel and the estimated attack signal reduces the effective malicious component entering the actuator. Based on Lyapunov-Krasovskii functionals, sufficient LMI-based conditions are derived for stability analysis and controller synthesis with [Formula: see text] performance. Finally, simulation results under different attack scenarios show that the proposed method attenuates FDI-induced frequency regulation errors and reduces unnecessary event-triggered transmissions.

This article focuses on the sliding mode bumpless transfer control (SMBTC) problem for switched systems with disturbance under mode-dependent average dwell time (MDADT) constraints. Compared with the existing results, this study establishes a variable structure bumpless transfer control scheme by combining the sliding mode control (SMC) method and the bumpless transfer technique together to effectively deal with the disturbance and bumps of control input for switched systems. First, a novel dual-mode transition-dependent SMBTC strategy consisting of the flexible bumpless transfer control and robust control is proposed for the reachability of a predefined mode-dependent sliding surface. Then, by constructing the dual mode-dependent Lyapunov functions, sufficient conditions are proposed for the global uniform asymptotical stability of resultant sliding mode dynamics (SMDs) under the MDADT constraints, which allows the system energy to be nondecreasing during the bumpless transfer stage and thus improves the freedom of control synthesis. Furthermore, considering that the steady-state properties of systems are imposed on the sliding surface, the bumpless transfer performance in the sliding phase is discussed as a special case by partly relaxing the bumps limitation. Finally, the feasibility and superiority of the presented results are demonstrated by a practical example of aero-engines.