Optimization of hybrid dynamic systems typically involves characterizing switching times and mode sequences. Operating autonomous hybrid systems with varying event timings presents multiple challenges. Complexity often arises from optimal mode sequence determination, making optimization of the corresponding hybrid automaton more difficult. An experimental autonomous hybrid dynamic system experiencing switching due to choked flow conditions is presented. Implementing gradient-based optimization algorithms may be difficult due to complex switching patterns of the hybrid dynamic systems. To mitigate this, an approximation of the Heaviside step function is applied to transform the hybrid switching functions to a continuous and smooth forms. Using the Control Vector Parameterization (CVP) approach and evaluating gradients using the variational method, an open-loop time-optimal control problem is presented. Modeling and control methods are demonstrated using an experimental two-tank air system. The optimal control formulation can include constraints to avoid specific undesirable modes of operation.

We have proposed a Generalized Descent Symmetrical Hestenes-Stiefel algorithm [12] , GDSHS for short, which can generate sufficient descent directions for the objective function. Using the Wolfe line search conditions, the global convergence property of the method is also obtained based on the spectral analysis of the conjugate gradient iteration matrix and the Zoutendijk condition for steepest descent methods. I propose in this paper a theoretical choice to improve the performance of the GDSHS algorithm, by the use of an optimal parameter. Based on this, some descent algorithms are developed. 86 numerical experiments are presented to verify their performance and the numerical results show that the new conjugate gradient method GDSHS with the parameter c=1 , denoted GDSHS1, is competitive with GDSHS algorithms that have a parameter c chosen in the interval ] 0 , + ∞ [ .

In this article, a fractional-order sliding mode control (FOSMC) method is presented for a wind energy conversion system (WECS) with variable-speed direct-drive permanent magnet synchronous generator (PMSG) under both normal and fault conditions. Under normal operation of the system, the machine side converter (MSC) is employed to meet maximum power point tracking (MPPT) requirements of the wind turbine and the grid side converter (GSC) controls the DC-link voltage and the injected reactive. Under fault condition, to meet grid code obligations, such as low voltage ride through (LVRT), the MSC adjusts the DC-link voltage instead of the GSC. Meanwhile, the active and reactive powers are controlled by the GSC. Moreover, the suggested control method is compared to the conventional control system. The results depicted that the proposed control approach has better faster dynamic response and robustness under both balanced and unbalanced condition. In addition, improving LVRT capability and injecting reactive power, the suggested control method results in smaller spikes in the injected current and DC link voltage. For the sake of further validation, simulations are run in offline MATLAB/Simulink simulation. Then, the results have been validated via experimental real-time implementation.

The current crisis of global climate change and its consequences which are manifested in form of different environmental disasters is attributed to excessive emission and accumulation of greenhouse gases in the atmosphere, key among which is carbon dioxide. Hence, remedies are needed to mitigate against this change in climate. A mathematical model on climate change incorporating good conservation policies, enlightenment programmes and direct air capture technology as mitigation measures is formulated and analysed using the concept of optimal control theory and cost-effectiveness analysis. The objective functional is set up to minimize both the excessive concentration of carbon dioxide in the atmosphere and the total cost of implementation of each mitigation measure, as the resources available to cater for the needs of the teeming human population are limited. By formulating a Hamiltonian function and using Pontryagin’s Principle, the adjoint equations and characterisation of the optimal units were calculated. Using the optimality control system obtained, the numerical simulation was done in MATLAB using the Forward Backward Sweep algorithm of the Runge-Kutta Method. Seven different strategies of mitigation scenarios were simulated. From the results, each of these strategies has the potency to reduce the excessive concentration of carbon dioxide in the atmosphere. However, the best result was obtained using the strategy that combines all the three mitigation measures of good conservation policies, enlightenment programmes and direct air capture technology. Despite that this strategy (Strategy VII) appears the most desirable option to adopt, the cost of implementation of each strategy has to be considered since human resources are limited. Therefore, cost-effectiveness analysis techniques (Average Cost-Effectiveness Ratio and Incremental Cost-Effectiveness Ratio ) were used to arrive at the most cost-friendly strategy. From the computations involving these two ratios, both indicated good conservation policies strategy as the cheapest option to adopt in reducing the excessive concentration of carbon dioxide in the atmosphere.

The necessary conditions for the optimal control of partially observed, fully coupled forward-backward mean-field stochastic differential equations driven by Teugels martingales are discussed in this paper. In this context, we make the assumption that the forward diffusion coefficient and the martingale coefficient are independent of the control variable, and the control domain may not necessarily be convex. For this class of optimal control problems, we derive the stochastic maximum principle based on the classical method of spike variations and the filtering techniques. The adjoint processes that are related to the variational equations are determined by the solutions of proposed forward-backward stochastic differential equations in finite-dimensional spaces. Further, the Hamiltonian function is used to obtain the maximum principle for the optimality of the given control system. Our results are then applied to the mean-field type problem of linear quadratic stochastic optimization.

In this article, a model-free parallel reinforcement learning method is proposed to solve the suboptimal control problem for the Markov jump singularly perturbed systems. First, since fast and slow dynamics coexist in Markov jump singularly perturbed systems, it may lead to ill-conditioned numerical problems during the controller design process. Therefore, the original system can be decomposed into independent subsystems at different time-scales by employing the reduced order method. Besides, a model-based parallel algorithm is designed to obtain the optimal controllers of the fast and slow subsystems respectively. Moreover, within the framework of reinforcement learning, the composite controller of the Markov jump singularly perturbed systems can be obtained without system dynamics. Finally, a numerical example is introduced to prove the effectiveness of proposed algorithms.

A new method is developed for accurately approximating the solution to state-variable inequality path constrained optimal control problems using a multiple-domain adaptive Legendre-Gauss-Radau collocation method. The method consists of the following parts. First, a structure detection method is developed to estimate switch times in the activation and deactivation of state-variable inequality path constraints. Second, using the detected structure, the domain is partitioned into multiple-domains where each domain corresponds to either a constrained or an unconstrained segment. Furthermore, additional decision variables are introduced in the multiple-domain formulation, where these additional decision variables represent the switch times of the detected active state-variable inequality path constraints. Within a constrained domain, the path constraint is differentiated with respect to the independent variable until the control appears explicitly, and this derivative is set to zero along the constrained arc while all preceding derivatives are set to zero at the start of the constrained arc. The time derivatives of the active state-variable inequality path constraints are computed using automatic differentiation and the properties of the chain rule. The method is demonstrated on two problems, the first being a benchmark optimal control problem which has a known analytical solution and the second being a challenging problem from the field of aerospace engineering in which there is no known analytical solution. When compared against previously developed adaptive Legendre-Gauss-Radau methods, the results show that the method developed in this paper is capable of computing accurate solutions to problems whose solution contain active state-variable inequality path constraints.

The main objective of this study is to address the challenge of simultaneously ensuring robustness and convergence performance in model-free inversion-based iterative learning control. Initially, this research provides a mathematical analysis of the sources of errors in the iterative process, followed by proposing a design guideline to enhance both convergence speed and the final value error. Based on the design guideline, a gain design method associated with the number of iterations is proposed, resulting in a novel model-free inversion-based iterative learning control algorithm. Subsequently, a robustness analysis of the proposed algorithm is conducted. Finally, a comprehensive simulation and numerical comparison of the proposed algorithm with existing similar algorithms are presented to demonstrate the superior performance of the proposed control algorithm.

We introduce the theoretical framework from geometric optimal control for a control system modeled by the Generalized Lotka-Volterra (GLV) equation, motivated by restoring the gut microbiota infected by Clostridium difficile combining antibiotic treatment and fecal injection. We consider both permanent control and sampled-data control related to the medical protocols.