Academic literature on the topic 'Multi-modes switching problem'

This paper studies the problem of the deterministic version of the Verification Theorem for the optimal m-states switching in infinite horizon under Markovian framework with arbitrary switching cost functions. The problem is formulated as an extended impulse control problem and solved by means of probabilistic tools such as the Snell envelop of processes and reflected backward stochastic differential equations. A viscosity solution approach is employed to carry out a fine analysis on the associated system of m variational inequalities with inter-connected obstacles. We show that the vector of value functions of the optimal problem is the unique viscosity solution to the system. This problem is in relation with the valuation of firms in a financial market.

We study a finite horizon optimal multi-modes switching problem with many nodes. The switching is based on the optimal expected profit and cost yields, moreover both sides of the balance sheet are considered. The profit and cost yields per unit time are respectively assumed to be coupled through a coupling term which is the average of profit and cost yields. The corresponding system of Snell envelopes is highly complex, so we consider the aggregated yields where a mean-field approximation is used for the coupling term. First, the problem is formulated by the mean of the Snell envelope of processes. Then, in terms of backward SDEs, the problem is equivalent to a system of mean-field reflected backward SDEs with interconnected and nonlinear obstacles. More precisely, the driver function depends also on the mean of the unknown process (expected profit or cost yields) which makes the mean-field interaction in the driver nonlinear. The first main result of this paper, is to show the existence of a continuous minimal solution of the system of mean-field reflected backward SDEs, which is done by using the Picard iteration method. The second main result concerns the optimality of the switching strategies which we fully characterize.

This article focuses on the tracking and stabilizing issues of a class of discrete switched systems. These systems are characterized by unknown switching sequences, a non-minimum phase, and time-varying or dead modes. In particular, for those governed by an indeterminate switching signal, it is very complicated to synthesize a control law able to systematically approach general reference-tracking difficulties. Taking into account the difficulty to express the dynamic of this class of systems, the present paper presents a new Dynamic matrix control method based on the multi-objective optimization and the truncated impulse response model. The formulation of the optimization problem aims to approach the general step-tracking issues under persistent and indeterminate mode changes and to overcome the stability problem along with retaining as many desirable features of the standard dynamic matrix control (DMC) method as possible. In addition, the formulated optimization problem integrates estimator variables able to manipulate the optimization procedure in favor of the active mode with an appropriate adjustment. It also provides a progressive and smooth multi-objective control law even in the presence of problems whether in subsystems or switching sequences. Finally, simulation examples and comparison tests are conducted to illustrate the potentiality and effectiveness of the developed method.

As renewable energy sources connecting to power systems continue to improve and new-type loads, such as electric vehicles, grow rapidly, direct current (DC) microgrids are attracting great attention in distribution networks. In order to satisfy the voltage stability requirements of island DC microgrids, the problem of inaccurate load power dispatch caused by line resistance must be solved and the defects of centralized communication and control must be overcome. A hierarchical, coordinated, multiple-mode control strategy based on the switch of different operation modes is proposed in this paper and a three-layer control structure is designed for the control strategy. Based on conventional droop control, a current-sharing layer and a multi-mode switching layer are used to ensure the stable operation of the DC microgrid. Accurate load power dispatch is satisfied using a difference discrete consensus algorithm. Furthermore, virtual bus voltage information is applied to guarantee smooth switching between various modes, which safeguards voltage stability. Simulation verification is carried out for the proposed control strategy by power systems computer aided design/electromagnetic transients including DC (PSCAD/EMTDC). The results indicate that the proposed control strategy guarantees the voltage stability of island DC microgrids and accurate load power dispatch under different operation modes.

According to the switch transients problem existing in the Hybrid Actuation System (HAS), a multi-mode switching control system was proposed. This control system, based on the system feedback correction theory, can cater to the demands of dynamic characteristics and switch transients. To start with, the mathematical model of HAS was established on the basic of HASs operating principle, and the HAS is composed of Hydraulic Servo Actuator (HSA) and Electro-Hydrostatic Actuator (EHA). Further, the different operating modes controller are hammered out by employed the PID feedback correction control, and the acceleration feedback controller is added to the switched system to decreasing the switch transients. Finally, simulation results demonstrate the system is precise in tracking displacement signal, and it is validity of mitigating the switch transients by used method of feedback correction.

To alleviate the mode mismatch of multiple model methods for nonlinear systems when completely discrete dynamical equations are adopted, a semi-continuous piecewise affine (SCPWA) model based optimal control method is proposed. Firstly, a SCPWA model is constructed where modes evolve in continuous time and continuous states evolve in discrete time. Thanks to this model, a piecewise affine (PWA) system can switch at any time instant whereas mode switching only occurs at sample instants when a completely discrete PWA model is adopted, which improves the prediction accuracy of multi-models. Secondly, the switching condition is relaxed such that operating subspaces have overlaps and switching condition parameters are introduced. As a consequence, an optimal control problem with fixed mode switching sequence is established. Finally, a SCPWA model based model predictive control (MPC) policy is designed for nonlinear systems. The convergence of the MPC algorithm is proved. Compared with widely used mixed logical dynamic (MLD) model based methods, the proposed method not only alleviates mode mismatch, but also lightens the computing burden, hence improves the control performance and reduces the computation time. Some numerical examples are provided as well to show the efficiency of the method.

The problem of reliable control for variable fault systems under linear quadratic Gaussian (LQG) framework is studied in this paper. Firstly, a cluster of models is used to cover the dynamic behaviors of different fault modes of a system and, for each model, LQG control is implemented. By using the a posteriori probability of model innovation as the weight information, a multi-model reliable control (MMRC) is proposed. Secondly, it is proved that MMRC can enable the controller to learn the real operating mode of the system. When the controller is in a deadlock state, a deadlock avoidance strategy is given and its convergence of the a posteriori probability is proved. Finally, the validity of MMRC is verified by an example simulation of the lateral-directional control system of an aircraft. Simulation results show that MMRC guarantees an acceptable performance of the closed-loop system. In addition, since the controller fuses the control law of each model according to the weight information, when the system model is switched, the controller implements a soft switching, which avoids the jitter caused by frequent hard switching to the system.

Cette thèse est composée de trois parties. Dans la première nous montrons l'existence et l'unicité de la solution continue et à croissance polynomiale, au sensviscosité, du système non linéaire de m équations variationnelles de type intégro-différentiel à obstacles unilatéraux interconnectés. Ce système est lié au problème du switching optimal stochastique lorsque le bruit est dirigé par un processus de Lévy. Un cas particulier du système correspond en effet à l’équation d’Hamilton-Jacobi-Bellman associé au problème du switching et la solution de ce système n’est rien d’autre que la fonction valeur du problème. Ensuite, nous étudions un système d’équations intégro-différentielles à obstacles bilatéraux interconnectés. Nous montrons l’existence et l’unicité des solutions continus à croissance polynomiale, au sens viscosité, des systèmes min-max et max-min. La démarche conjugue les systèmes d’EDSR réfléchies ainsi que la méthode de Perron. Dans la dernière partie nous montrons l’égalité des solutions des systèmes max-min et min-max d’EDP lorsque le bruit est uniquement de type diffusion. Nous montrons que si les coûts de switching sont assez réguliers alors ces solutions coïncident. De plus elles sont caractérisées comme fonction valeur du jeu de switching de somme nulle
There are three main results in this thesis. The first is existence and uniqueness of the solution in viscosity sense for a system of nonlinear m variational integral-partial differential equations with interconnected obstacles. From the probabilistic point of view, this system is related to optimal stochastic switching problem when the noise is driven by a Lévy process. As a by-product we obtain that the value function of the switching problem is continuous and unique solution of its associated Hamilton-Jacobi-Bellman system of equations. Next, we study a general class of min-max and max-min nonlinear second-order integral-partial variational inequalities with interconnected bilateralobstacles, related to a multiple modes zero-sum switching game with jumps. Using Perron’s method and by the help of systems of penalized unilateral reflected backward SDEs with jumps, we construct a continuous with polynomial growth viscosity solution, and a comparison result yields the uniqueness of the solution. At last, we deal with the solutions of systems of PDEs with bilateral inter-connected obstacles of min-max and max-min types in the Brownian framework. These systems arise naturally in stochastic switching zero-sum game problems. We show that when the switching costs of one side are smooth, the solutions of the min-max and max-min systems coincide. Furthermore, this solution is identified as the value function of the zero-sum switching game