scholarly journals Nonsmooth optimization over the (weakly or properly) Pareto set of a linear-quadratic multi-objective control problem: Explicit optimality conditions

2011 ◽  
Vol 7 (4) ◽  
pp. 789-809 ◽  
Author(s):  
Henri Bonnel ◽  
◽  
Ngoc Sang Pham
Keyword(s):  
Control Problem ◽  
Optimality Conditions ◽  
Nonsmooth Optimization ◽  
Pareto Set ◽  
Linear Quadratic ◽  
Multi Objective ◽  
Objective Control

Urban Oversaturated Traffic Network Control Based on Preference Multi-Objective Compatible Optimization Control

2011 ◽  
Vol 317-319 ◽  
pp. 1373-1384 ◽  
Author(s):  
Juan Chen ◽  
Chang Liang Yuan
Keyword(s):  
Control Problem ◽  
Control Algorithm ◽  
Control Method ◽  
Network Control ◽  
Feasible Region ◽  
Traffic Network ◽  
Total Delay ◽  
Multi Objective ◽  
Optimization Control ◽  
Objective Control

To solve the traffic congestion control problem on oversaturated network, the total delay is classified into two parts: the feeding delay and the non-feeding delay, and the control problem is formulated as a conflicted multi-objective control problem. The simultaneous control of multiple objectives is different from single objective control in that there is no unique solution to multi-objective control problems(MOPs). Multi-objective control usually involves many conflicting and incompatible objectives, therefore, a set of optimal trade-off solutions known as the Pareto-optimal solutions is required. Based on this background, a modified compatible control algorithm(MOCC) hunting for suboptimal and feasible region as the control aim rather than precise optimal point is proposed in this paper to solve the conflicted oversaturated traffic network control problem. Since it is impossible to avoid the inaccurate system model and input disturbance, the controller of the proposed multi-objective compatible control strategy is designed based on feedback control structure. Besides, considering the difference between control problem and optimization problem, user's preference are incorporated into multi-objective compatible control algorithm to guide the search direction. The proposed preference based compatible optimization control algorithm(PMOCC) is used to solve the oversaturated traffic network control problem in a core area of eleven junctions under the simulation environment. It is proved that the proposed compatible optimization control algorithm can handle the oversaturated traffic network control problem effectively than the fixed time control method.

scholarly journals Maximum Principle for Stochastic Recursive Optimal Control Problems Involving Impulse Controls

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Zhen Wu ◽  
Feng Zhang
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Control Variable ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Linear Quadratic ◽  
Regular Control

We consider a stochastic recursive optimal control problem in which the control variable has two components: the regular control and the impulse control. The control variable does not enter the diffusion coefficient, and the domain of the regular controls is not necessarily convex. We establish necessary optimality conditions, of the Pontryagin maximum principle type, for this stochastic optimal control problem. Sufficient optimality conditions are also given. The optimal control is obtained for an example of linear quadratic optimization problem to illustrate the applications of the theoretical results.

Multi-Objective Disturbance Attenuation Control for T-S Fuzzy System with Hard Constraints

2013 ◽  
Vol 313-314 ◽  
pp. 453-456
Author(s):  
Xing Quan Gao ◽  
De Hua Meng
Keyword(s):  
Control Problem ◽  
Fuzzy System ◽  
Actuator Saturation ◽  
Disturbance Attenuation ◽  
Control Technique ◽  
System Control ◽  
Lmi Optimization ◽  
Multi Objective ◽  
Hard Constraints ◽  
Objective Control

This paper exploits a multi-objective control technique for T-S fuzzy system with hard constraints, which include actuator saturation and state constraints resulting from some mechanical structure constraints. The disturbance attenuation performance is characterized H norm, while requirements for respecting hard constraints are specified by the generalized H2norm. The T-S fuzzy system control problem is then formulated in a mixed H /generalized H2control problem , and an state feedback solution is derived using LMI optimization.

Urban Oversaturated Traffic Network Control Based on Stability Preference Multi-Objective Compatible Optimization Control

2012 ◽  
Vol 151 ◽  
pp. 503-509
Author(s):  
Juan Chen ◽  
Qing Song Hu ◽  
Xiang Yang Sun
Keyword(s):  
Control Problem ◽  
Pareto Front ◽  
Control Method ◽  
Network Control ◽  
Selection Strategy ◽  
Traffic Network ◽  
Nsga Ii ◽  
Multi Objective ◽  
Optimization Control ◽  
Objective Control

To solve the traffic congestion control problem on oversaturated network, the control problem is formulated as a conflicted multi-objective control problem., a new stability preference multi-objective compatible optimization control(SPMOCC) algorithm is proposed to solve the conflicted multi-objective control problem. In the proposed SPMOCC algorithm, NSGA-II algorithm is adjusted by proposing non-even Pareto front spread preserving strategy to obtain some special area on the Pareto front; a stability preference selection strategy is proposed to obtain stable controller. The proposed SPMOCC is used to solve the oversaturated traffic network control problem in a core area of 11 junctions under the simulation environment. It is proved that the proposed compatible optimization control algorithm can handle the oversaturated traffic network control problem effectively than the fixed time control method.

Pareto Set as a Model for Dispatching Resources in Emergency Centres (Preprint)

2018 ◽  
Author(s):  
Ricardo Guedes ◽  
Vasco Furtado ◽  
Tarcísio Pequeno ◽  
Joel Rodrigues
Keyword(s):  
Operational Research ◽  
Real Data ◽  
Pareto Set ◽  
Multi Objective Optimization ◽  
Pareto Dominance ◽  
Four Dimensions ◽  
Multi Objective ◽  
The Best Approximation ◽  
One Year ◽  
The Cost

UNSTRUCTURED The article investigates policies for helping emergency-centre authorities for dispatching resources aimed at reducing goals such as response time, the number of unattended calls, the attending of priority calls, and the cost of displacement of vehicles. Pareto Set is shown to be the appropriated way to support the representation of policies of dispatch since it naturally fits the challenges of multi-objective optimization. By means of the concept of Pareto dominance a set with objectives may be ordered in a way that guides the dispatch of resources. Instead of manually trying to identify the best dispatching strategy, a multi-objective evolutionary algorithm coupled with an Emergency Call Simulator uncovers automatically the best approximation of the optimal Pareto Set that would be the responsible for indicating the importance of each objective and consequently the order of attendance of the calls. The scenario of validation is a big metropolis in Brazil using one-year of real data from 911 calls. Comparisons with traditional policies proposed in the literature are done as well as other innovative policies inspired from different domains as computer science and operational research. The results show that strategy of ranking the calls from a Pareto Set discovered by the evolutionary method is a good option because it has the second best (lowest) waiting time, serves almost 100% of priority calls, is the second most economical, and is the second in attendance of calls. That is to say, it is a strategy in which the four dimensions are considered without major impairment to any of them.

scholarly journals Convergence results for an averaged LQR problem with applications to reinforcement learning

2021 ◽  
Author(s):  
Andrea Pesare ◽  
Michele Palladino ◽  
Maurizio Falcone
Keyword(s):  
Optimal Control ◽  
Reinforcement Learning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Current System ◽  
Numerical Test ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Lqr Problem ◽  
Quadratic Optimal Control

AbstractIn this paper, we will deal with a linear quadratic optimal control problem with unknown dynamics. As a modeling assumption, we will suppose that the knowledge that an agent has on the current system is represented by a probability distribution $$\pi $$ π on the space of matrices. Furthermore, we will assume that such a probability measure is opportunely updated to take into account the increased experience that the agent obtains while exploring the environment, approximating with increasing accuracy the underlying dynamics. Under these assumptions, we will show that the optimal control obtained by solving the “average” linear quadratic optimal control problem with respect to a certain $$\pi $$ π converges to the optimal control driven related to the linear quadratic optimal control problem governed by the actual, underlying dynamics. This approach is closely related to model-based reinforcement learning algorithms where prior and posterior probability distributions describing the knowledge on the uncertain system are recursively updated. In the last section, we will show a numerical test that confirms the theoretical results.

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