Search results for "Mathematical optimization"
showing 10 items of 1300 documents
Stationary and Initial-Terminal Value Problem for Collective Decision Making via Mean-Field Games
2017
Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, following some optimality criteria. The optimal transition rates are based on the players' knowledge of their current state and of the distribution of all the other players, thus introducing mean-field terms in the running and the terminal cost. The first contribution is a mean-field model that takes into account the macroscopic and the microscopic dynamics. The second contribution is the study of the mean-field equilibrium resulting from solving the initial-terminal value problem, involving the Kolmogorov equat…
A Lyapunov–Razumikhin approach for stability analysis of logistics networks with time-delays
2012
Logistics network represents a complex system where different elements that are logistic locations interact with each other. This interaction contains delays caused by time needed for delivery of the material. Complexity of the system, time-delays and perturbations in a customer demand may cause unstable behaviour of the network. This leads to the loss of the customers and high inventory costs. Thus the investigation of the network on stability is desired during its design. In this article we consider local input-to-state stability of such logistics networks. Their behaviour is described by a functional differential equation with a constant time-delay. We are looking for verifiable conditio…
A new fuzzy robust dynamic controller for autonomous vehicles with nonholonomic constraints
2005
Abstract In this paper a novel algorithm with a dynamic fuzzy controller applied to the control of trajectory of vehicles with two independent wheels is proposed. An automatic control of trajectory of a vehicle can behave in a not efficient way. It is necessary to consider the friction of the actuators and possible perturbations coming from the outside environment, as for instance the variable characteristics of the ground where the vehicle moves. These perturbations, which depend also on the contact between the wheel and the ground, involve violations of nonholonomic constraints. Thus it is necessary to compensate for these perturbations to obtain a robust control system. The controller sy…
Control of uncertain highly nonlinear biological process based on Takagi–Sugeno fuzzy models
2015
This note deals with the control of uncertain highly nonlinear biological processes. Indeed, an adaptive fuzzy control (AFC) scheme is developed for the pre-treatment of wastewater represented by a Takagi-Sugeno (TS) fuzzy model. The proposed approach uses a fuzzy system to approximate the unknown substrate consumption rate in designing the adaptive controller, and then an observer is designed to estimate the concentration in substrate at the outlet bioreactor. The observer is employed to generate an error signal for the adaptive control law which permits to minimize the influence of the measurement noise on the estimation of the substrate concentration. An update of the fuzzy models parame…
Dynamic Resource Allocation and Computation Offloading for Edge Computing System
2020
In this work, we propose a dynamic optimization scheme for an edge computing system with multiple users, where the radio and computational resources, and offloading decisions, can be dynamically allocated with the variation of computation demands, radio channels and the computation resources. Specifically, with the objective to minimize the energy consumption of the considered system, we propose a joint computation offloading, radio and computational resource allocation algorithm based on Lyapunov optimization. Through minimizing the derived upper bound of the Lyapunov drift-plus-penalty function, the main problem is divided into several sub-problems at each time slot and are addressed sepa…
Observer-based adaptive stabilization of a class of uncertain nonlinear systems
2014
In this paper, an adaptive output feedback stabilization method for a class of uncertain nonlinear systems is presented. Since this approach does not require any information about the bound of uncertainties, this information is not needed a priori and a mechanism for its estimation is exploited. The adaptation law is obtained using the Lyapunov direct method. Since all the states are not measurable, an observer is designed to estimate unmeasurable states for stabilization. Therefore, in the design procedure, first an observer is designed and then the control signal is constructed based on the estimated states and adaptation law with the σ-modification algorithm. The uniformly ultimately bou…
Robust control of continuous-time systems with state-dependent uncertainties and its application to electronic circuits
2014
In this paper, the problems of robust stability and stabilization are investigated for a class of continuous-time uncertain systems. The uncertainties in the model are state-dependent and belong to a polytopic convex set, as can be found in many electronic circuits and some other applications. The global asymptotic stability conditions for such systems are first established by the classic common quadratic Lyapunov function approach. To reduce conservativeness, a particular class of nonquadratic parameter-dependent Lyapunov functions is introduced, by which improved robust stability conditions for the underlying systems are also derived. Based on the stability criteria, a static output feedb…
Non-linear protocols for optimal distributed consensus in networks of dynamic agents
2006
We consider stationary consensus protocols for networks of dynamic agents with fixed topologies. At each time instant, each agent knows only its and its neighbors'' state, but must reach consensus on a group decision value that is function of all the agents'' initial state. We show that the agents can reach consensus if the value of such a function is time-invariant when computed over the agents'' state trajectories. We use this basic result to introduce a non-linear protocol design rule allowing consensus on a quite general set of values. Such a set includes, e.g., any generalized mean of order p of the agents'' initial states. As a second contribution we show that our protocol design is t…
Local capacity H<inf>∞</inf> control for production networks of autonomous work systems with time-varying delays
2009
This paper considers the problem of local capacity H ∞ control for a class of production networks of autonomous work systems with time-varying delays in the capacity changes. The system under consideration is modelled in a discrete-time singular form. Attention is focused on the design of a controller gain for the local capacity adjustments which maintains the work in progress (WIP) in each work system in the vicinity of planned levels and guarantees the asymptotic stability of the system and reduces the effect of the disturbance input on the controlled output to a prescribed level. In terms of a matrix inequality, a sufficient condition for the solvability of this problem is presented usin…
Design on fuzzy control for a class of stochastic nonlinear systems
2014
The problem of Hankel-norm output feedback control is solved for a class of T-S fuzzy stochastic systems. The dynamic output feedback controller design technique is proposed by employing fuzzy-basis-dependent Lyapunov function approach and the conversion on the Hankel-norm controller parameters. Sufficient conditions are established to design the controllers such that the resulting closed-loop system is stochastically stable and satisfies a prescribed performance. The desired output feedback controller can be obtained by solving a convex optimization problem, which can be efficiently solved by standard numerical algorithms Refereed/Peer-reviewed