Constrained Control Variables Research Articles

Robust optimal investment and reinsurance to minimize a goal-reaching probability with constrained control variables

This paper considers a robust optimal investment and reinsurance problem with constraints for an Ambiguity-Averse Insurer (AAI). The criterion is to minimize the goal-reaching probability, namely, the probability that the value of the wealth process reaches a low barrier before a high goal. The robust optimal investment-reinsurance strategy and closed-form expression of the associated value function are derived explicitly by applying stochastic dynamic programming and solving the corresponding Hamiliton-Jacobi-Bellman (HJB) equation. It is extremely interesting that the sum of our value function and the value function of Luo et al. [23] is equal to 1 in two cases of ambiguity and ambiguity-neutral. Finally, numerical examples are given to illustrate the influence of typical parameters on our results.

Variance constrained trajectory tracking for tandem-rotor helicopters

PurposeThis paper aims to present novel results for trajectory tracking of tandem-rotor helicopters via variance-constrained controllers.Design/methodology/approachRegarding these purposes, linearized tandem-rotor helicopter models are benefitted.FindingsVariance-constrained controllers are very beneficial for trajectory tracking of tandem-rotor helicopters while there exists variance bounds on outputs of interest.Practical implicationsVariance-constrained controllers can be used for cheaper tandem-rotor helicopter operations with high trajectory tracking quality.Originality/valueApplying variance-constrained control strategy for tandem-rotor helicopters during trajectory tracking. This also causes less fuel consumption and green environment, and good trajectory tracking quality.

Optimization of non-circular failure surface in slope based on particle swarm models

This article presents results of slope analyses employing a simple technique of generating segmented non-circular failure surfaces. The formulation of slope analysis is performed as an optimization problem with four constrained control variables characterizing the failure surface. In this study, different variants of particle swarm optimization (PSO) methods such as inertia weight equipped and contemporary standard PSO (CS-PSO) are utilized to obtain optimum control variables and associated critical failure surface. The factor of safety of the slope or the objective function of the constrained optimization problem is determined by Morgenstern–Price method. To explore the competence of proposed method with different PSO models, three benchmark problems are analysed for different maximum number of function evaluations such as 1000, 2500 and 5000. A series of sensitivity analyses are performed for various parameters such as swarm size with maximum iteration count of 100. The swarm diversity behaviour is also studied in relation with converged or promising global optimum solution. It is found that contemporary standard PSO (CS-PSO) with or without velocity clamping maintains better swarm diversity and preserves the balance between swarm “exploration” and “exploitation” efficiently. Velocity clamping and positional clamping are recommended as they prevent the solution/control variable from overflying the swarm best position.

Optimal Control for Reducing Congestion and Improving Safety in Freeway Systems

The efficiency of freeway systems is often hindered by recurrent and non-recurrent congestion. The occurrence of these events is due not only to the high number of vehicles trying to use a shared infrastructure, but also by phenomena that temporarily deteriorate the capacity of the infrastructure itself. Among them, road accidents are considered as one of the primary causes of non-recurrent congestion. At the same time, several studies also identify traffic breakdowns as events leading to vehicle crashes. A specific goal of this research is to develop a global safety index that quantifies the expected number of crashes as a function of the current traffic state in the freeway system. Moreover, on the basis of this new index and the performance indicator generally adopted to evaluate the traffic delay, a coordinated ramp metering scheme is proposed jointly considering the reduction of travel times for the drivers and the improvement of safety in the freeway system. The control strategy is sought by defining a nonlinear optimal control problem with constrained control variables, solved by applying a specific gradient-based algorithm. The simulation analysis investigates the multi-objective nature of the problem assessing whether and to what extent the two components of the cost criterion are conflicting objectives.

Variance and passivity constrained sliding mode fuzzy control for continuous stochastic non-linear systems

A multiple performance constrained sliding mode fuzzy control problem is investigated in this paper for continuous-time stochastic non-linear systems. The stability constraint, passivity constraint and individual state variance constraint are simultaneously considered in this paper. By combining sliding mode control, variance constrained control and model-based fuzzy control, a novel performance constrained fuzzy control approach is developed. Applying Lyapunov function, some sufficient conditions are derived in term of linear matrix inequalities that can be solved by convex optimal programming algorithm. The main contribution of this paper is to develop a parallel distributed compensation based sliding mode fuzzy controller such that closed-loop system can achieve multiple performance constraints. At last, a numerical example for the control of translational oscillations with a rotational actuator system is given to demonstrate the validity and effectiveness of proposed sliding mode fuzzy control method.

Optimal investment and proportional reinsurance for a jump–diffusion risk model with constrained control variables

This paper considers the optimal control problem with constraints for an insurer. The risk process is assumed to be a jump–diffusion process, and the risk can be reduced through a proportional reinsurance. In addition, the surplus can be invested in the financial market consists of one risk-free asset and one risky asset. The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. This optimization problem is studied in two cases depending on the diffusion term’s explanations. In all cases, with normal constraints on the control variables, the value functions and the corresponding optimal strategies are given in a closed form. Numerical simulations are presented to illustrate the effects of parameters on the optimal strategies as well as the economic meaning behind.

Combined passive and active helicopter main rotor morphing for helicopter energy save

In this article, passive morphing and active morphing approaches are combined to save more helicopter flight control system (i.e., FCS) energy. For this purpose complex, physics-based, control-oriented nonlinear helicopter models are benefited. A specific variance-constrained control strategy, namely Output Variance-Constrained Control (i.e., OVC) is applied for helicopter FCS. Control energy savings using passive, active and combined morphing approaches are examined. Parameters of helicopter FCS and combined morphing helicopter design parameters are simultaneously optimized using a stochastic optimization method, namely simultaneous perturbation stochastic approximation (i.e., SPSA). To observe energy save, closed-loop analyses are done. Finally, robustness of combined morphing helicopter with respect to (w.r.t.) the modeling uncertainties is examined.

Robust Static Output Feedback Control for Switched Systems with Input Constraints

In the paper, an LMI robust static output feedback (SOF) controller design procedure for switched discrete-time systems with constrained control variables is proposed, based on previous results on SOF controller design and input constraint control. The heuristic iterative procedure is described, using linearization to receive LMI conditions. The proposed SOF controller design is illustrated on a case study of two tank switched system.

Variance-Constrained Multiobjective Control and Filtering for Nonlinear Stochastic Systems: A Survey

The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixedH2/H∞control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out.

Variance-constrained control of maneuvering helicopters with sensor failure

This article presents the novel results obtained using variance-constrained controllers and maneuvering helicopters also when some helicopter sensors fail. For this purpose, complex, control oriented, and physics-based helicopter models are used. A nonlinear model of the helicopter, which includes blade flexibility, is first linearized around specific maneuvering flight conditions (i.e. level banked turn and helical turn). The resulting linearized models are used for the design of variance-constrained controllers (i.e. output and input variance-constrained controllers). Then, the robustness of the closed-loop systems with respect to modeling uncertainties (i.e. flight conditions and helicopter inertial parameters variations) is studied. Next, variance-constrained controllers are designed for these maneuvering helicopter models when some helicopter sensors fail. Several sensor failure cases are examined and robustness properties of the closed-loop systems with respect to modeling uncertainties are also examined. Limitations of the control design process due to the number and type of failed sensors are investigated as well. Finally, the possibility to adaptively switch between controllers in order to mitigate sensor failure is studied.

Robust Variance-Constrained Control for a Class Continuous Markov Jump Systems

For a class continuous Markov jump systems, the variance-constrained and uncertain robust performance problem is researched, which guarantees the closed-loop steady-state variance to be less than a given upper, and the conditions for the existence of such controllers are proposed and proved. The designed method of these controllers is proposed. The simulation results show that the designed controller meets the demands of stability, robustness and varianceconstrained.

Integrated route guidance and ramp metering consistent with drivers' en-route diversion behaviour

The primary focus of this study is to present a new integrated traffic control model for urban freeways using model-based predictive control (MPC) framework, where the effect of traffic information on drivers' en-route diversion behaviour is explicitly modelled using an adaptive constrained Kalman filtering theory. This captures the effect of traffic information on drivers' real-time en-route diversion behaviour, based on on-line traffic surveillance data. The integrated control task is formulated as a dynamic, non-linear, discrete time optimal control problem with constrained control variables. The network traffic flow process is modelled by a dynamic network traffic flow model, which is deterministic, discrete in time and space, macroscopic and suitable for model-based traffic control. Feedback control is realised by solving the optimisation problem for each control interval over a long future-time horizon. Simulation results for a case study show that the proposed integrated MPC model takes in consideration of the time-dependent traffic characteristics and drivers' actual behaviour and can significantly enhance the traffic efficiency and reduce the cost of traffic system by 17.1-30.0%.

Optimal investment and proportional reinsurance with constrained control variables

AbstractIn this paper, under the criterion of maximizing the expected exponential utility from terminal wealth, we study the optimal investment and proportional reinsurance strategy for an insurance company. The closed‐form expressions for the optimal strategy and value function are derived not only for the compound Poisson risk model but also for the Brownian motion model. We can see that, with normal constraints on the control variables, the value function is still a classical solution to the corresponding Hamilton–Jacobi–Bellman equation. Copyright © 2010 John Wiley & Sons, Ltd.

Robust Variance-constrained Control of a Class of Stochastic Hybrid Systems

摘要: 对一类结构参数不完全已知的Markov跳变参数系统, 研究使得闭环系统的稳态状态方差小于某个给定的上界, 同时满足一定H∞性能的状态反馈鲁棒方差控制器设计问题. 运用线性矩阵不等式(Linear matrix inequality, LMI)方法, 对系统进行了方差分析, 给出并证明了控制器存在的条件, 进而用一组线性矩阵不等式的可行解给出了控制器的一个参数化表示. 通过建立一个具有LMI约束的凸优化问题, 给出了最小方差鲁棒控制器的设计方法. 最后仿真结果表明了该方法的有效性. 关键词: 方差约束 / H∞性能 / 容错控制系统 / Markov跳变系统 / 乘性噪声

Robust variance-constrained control for a class of continuous time-delay systems with parameter uncertainties

In this paper, we consider the robust variance-constrained control problem for uncertain linear continuous time-delay systems subjected to parameter uncertainties. The purpose of this multi-objective control problem is to design a static state feedback controller that does not depend on the parameter uncertainties such that the resulting closed-loop system is asymptotically stable and the steady-state variance of each state is not more than the individual pre-specified value simultaneously. Using the linear matrix inequality approach, the existence conditions of such controllers are derived. A parameterized representation of the desired controllers is presented in terms of the feasible solutions to a certain linear matrix inequality system. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed results.

Variance-Constrained Control for Uncertain Stochastic Systems With Missing Measurements

In this paper, we are concerned with a new control problem for uncertain discrete-time stochastic systems with missing measurements. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The system measurements may be unavailable (i.e., missing data) at any sample time, and the probability of the occurrence of missing data is assumed to be known. The purpose of this problem is to design an output feedback controller such that, for all admissible parameter uncertainties and all possible incomplete observations, the system state of the closed-loop system is mean square bounded, and the steady-state variance of each state is not more than the individual prescribed upper bound. We show that the addressed problem can be solved by means of algebraic matrix inequalities. The explicit expression of the desired robust controllers is derived in terms of some free parameters, which may be exploited to achieve further performance requirements. An illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach.

Discrete-time inventory models with deteriorating items

The discrete-time inventory control problem for deteriorating items with deterministic or stochastic demand is considered. The control problem is stated as an optimization problem with constrained control variables. The linear quadratic (LQ) criterion is used to derive the optimal control policy for both deterministic and stochastic demand cases. In the presence of bounded uncertainties, a guaranteed cost control law is also proposed. A numerical example is provided to show the usefulness of the theoretical results.

Motorway Network Control via Nonlinear Optimization

The on‐line application of nonlinear optimization methods for control in motorway networks is presented. The considered control measure is route diversion by Variable Message Signs (VMS). The control task is formulated as a dynamic, nonlinear, discrete‐time optimal control problem with constrained control variables and is solved by a gradient‐based search. A modified algorithm for the heuristic search of optimal discrete (binary value) control sequences is presented. Feedback control is realized by solving the optimization problem for each control interval over a sufficiently long future time horizon (certainty equivalent open‐loop feedback control). As a prerequisite, a state‐space description of the network traffic dynamics is derived from a macroscopic model as used also in the simulation program METANET. Simulation results for route diversion on a hypothetical example network are given. The required computational effort is quantified and the control benefits are given in terms of network performance and the switching frequency of VMS.

Motorway network control via nonlinear optimization

The on-line application of nonlinear optimization methods for control in motorway networks is presented. The considered control measure is route diversion by Variable Message Signs (VMS). The control task is formulated as a dynamic, nonlinear, discrete-time optimal control problem with constrained control variables and is solved by a gradient-based search. A modified algorithm for the heuristic search of optimal discrete (binary value) control sequences is presented. Feedback control is realized by solving the optimization problem for each control interval over a sufficiently long future time horizon (certainty equivalent open-loop feedback control). As a prerequisite, a state-space description of the network traffic dynamics is derived from a macroscopic model as used also in the simulation program METANET. Simulation results for route diversion on a hypothetical example network are given. The required computational effort is quantified and the control benefits are given in terms of network performance and the switching frequency of VMS.

Route diversion control in motorway networks via nonlinear optimization

The online application of nonlinear optimization methods to feedback control of motorway networks is presented. The considered control measure is route diversion via variable message signs (VMS). The control task is formulated as a dynamic, nonlinear, discrete-time optimal control problem with constrained control variables and is solved by a gradient based search. An algorithm for the heuristic search of optimal discrete (binary) control sequences is also presented. Feedback control is realized by solving the optimization problem for each control interval over a sufficiently long future time horizon (certainty equivalent open-loop feedback control). As a prerequisite, a state-space description of the network traffic dynamics is derived from a macroscopic model that is also used in the simulation program METANET. Simulation results for route diversion on a hypothetical example network are provided. The required computational effort is assessed and the control benefits are evaluated in terms of global network performance, switching frequency of VMS and user optimality.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>