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1.
This paper is concerned with stochastic linear control systems driven by fractional Brownian motions (fBms) with Hurst parameter H∈(1/2,1) and the cost functional is quadratic with respect to the state and control variables. Here, the integrals with respect to fBms are the type of Stratonovich integrals. A stochastic maximum principle as a necessary condition of the optimal control is derived. The adjoint backward stochastic differential equation (BSDE) is driven by the fBms and its underlying standard Brownian motions. The existence and uniqueness of the solution of adjoint BSDE is proved. The explicit form of the unique optimal control is obtained. 相似文献
2.
In this paper, we study a partially observed linear quadratic optimal control problem derived by stochastic differential delay equations. Combining backward separation method with stochastic filtering, we obtain optimal feedback regulators in some special cases. Some filtering results for anticipated backward stochastic differential equations are also developed by expressing the solutions of the anticipated backward stochastic differential equations as some Itô's processes. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
3.
Minimizing control energy in a class of bounded‐control linear‐quadratic regulator problems 
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下载免费PDF全文 V. Costanza P. S. Rivadeneira A. H. González 《Optimal control applications & methods.》2014,35(3):361-382
Minimal‐control‐energy strategies are substantiated and illustrated for linear‐quadratic problems with penalized endpoints and no state‐trajectory cost, when bounds in control values are imposed. The optimal solution for a given process with restricted controls, starting at a known initial state, is shown to coincide with the saturated solution to the unrestricted problem that has the same coefficients but starts at a generally different initial state. This result reduces the searching span for the solution: from the infinite‐dimensional set of admissible control trajectories to the finite‐dimensional Euclidean space of initial conditions. An efficient real‐time scheme is proposed here to approximate (eventually to find) the optimal control strategy, based on the detection of the appropriate initial state while avoiding as much as possible the generation and evaluation of state and control trajectories. Numerical (including model predictive control) simulations are provided, compared, and checked against the analytical solution to ‘the cheapest stop of a train’ problem in its pure‐upper‐bounded brake, flexible‐endpoint setting. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
4.
In this paper, we consider the linear‐quadratic control problem with an inequality constraint on the control variable. We derive the feedback form of the optimal control by the agency of the unconstrained linear‐quadratic control systems. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
5.
Muneomi Sagara Hiroaki Mukaidani Vasile Dragan 《Optimal control applications & methods.》2011,32(1):113-125
In this paper, the linear quadratic optimal stochastic control problem is investigated for multiparameter singularly perturbed stochastic systems in which N lower‐level fast subsystems are interconnected by a higher‐level slow subsystem. After establishing the asymptotic structure of the solution for the multiparameter stochastic algebraic Riccati equation (MSARE), a near‐optimal controller that is independent of small unknown parameters is obtained by neglecting these parameters. The stability of a closed‐loop stochastic system is investigated. Furthermore, it is shown that the resulting controller achieves an O(∥ν∥2) approximation to the optimal cost of the original optimal control problem. Finally, in order to demonstrate the efficiency of the proposed algorithm, a numerical example—a practical multi‐area power system—is solved. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
6.
Lalitesh Kumar Prawendra Kumar Sukhwinder Singh Dhillon 《Optimal control applications & methods.》2020,41(4):1267-1287
This article bestows the linear quadratic Gaussian (LQG)/Loop Transfer Recovery (LTR) optimal controller design for a perturbed linear system having insufficient information about systems states through a multiobjective optimization approach. A Kalman filter observer is required to estimate the unknown states at the output from the noisy data. However, the main downside of the LQG controller's is that its robustness cannot be guaranteed because it consists of linear quadratic regulator (LQR) and Kalman observer, and due to observer incorporation within the LQR framework results in loss of robustness which is undesirable. Therefore, it is necessary to recover the robustness by tuning the controller which further plays havoc with system performance and control effort for certain plants. The present work addresses the investigation of the trade-off between multiobjective indexes (formulated on the basis of robustness, optimal control, and performances) through three multiobjective optimization algorithms as NSGA-II, multiobjective simulated annealing and multiobjective particle swarm optimization. The tuned parameters meet the competitive multiobjective performance indexes that are verified through simulation results. The Pareto front with multiple solutions helps to design a robust controller depending on the weightage given to the respective performance indexes. Simulation results reveal that the proposed multiobjective control strategy helps in recovering the characteristics of LQG/LTR. 相似文献
7.
Optimal control is one of the most important methodologies for studies of dynamic systems in many areas of sciences, engineering and economics. Minimax optimal control is a special topic in the general framework of multiple optimal control problems. Minimax optimal control can be considered as a dynamic game with multiple players under the same system. In this paper, we develop a fast search for a minimax solution of multiple linear‐quadratic control problems. The algorithm improves the existing solution scheme by adjusting the multiple weighting coefficients in each iteration and also including updates for step‐size control. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
8.
Yuhang Li;Yuecai Han;Yanwei Gao; 《Optimal control applications & methods.》2024,45(1):321-335
In this paper, we consider the stochastic optimal control problem for moving average control system. The corresponding moving average stochastic differential equation is a kind of integral differential equations. We prove the existence and uniqueness of the solution of the moving average stochastic differential equations. We obtain the stochastic maximum principle of the moving average optimal control system by introducing a kind of generalized anticipated backward stochastic differential equations. We prove the existence and uniqueness of the solution of this adjoint equation, which is singular at 0. As an application, the linear quadratic moving average control problem is investigated to illustrate the main results. 相似文献
9.
On the basis of the theory of stochastic differential equations on a sublinear expectation space , we develop a stochastic maximum principle for a general stochastic optimal control problem, where the controlled state process is a stochastic differential equation driven by G‐Brownian motion. Furthermore, under some convexity assumptions, we obtain sufficient conditions for the optimality of the maximum in terms of the ‐function. Finally, applications of the stochastic maximum principle to the mean‐variance portfolio selection problem in the financial market with ambiguous volatility is discussed. 相似文献
10.
Majura F. Selekwa Renatus N. Mussa Able Chiteshe 《Optimal control applications & methods.》2003,24(6):331-345
The increasing congestion on urban streets demands traffic control signal timing to be well co‐ordinated and optimized even during the transition between timing patterns used in different periods of time‐of‐day (TOD). The TOD timing plans, defined by fixed‐time co‐ordination parameters, need to change from one TOD period to another. The current methods used in transitioning are aimed at achieving quick transition rather than optimizing traffic flow during the transition period. As a result, they generally cause increased vehicle delays during the transition period particularly for vehicles on the minor street, which face lengthened red times. This paper proposes a quadratic optimization method that can be used to reduce disutility measures to motorists during the transition period. The transition is modeled as a linear dynamic process, and the disutility measures are modeled as the sum of squares of the deviations of the co‐ordination parameters—that is, cycle length, phase split, and offset—from the optimal values during the transition. A linear quadratic (LQ) optimization technique of optimal control is used to determine the step size and the number of steps necessary to complete the transition with minimum disutility. The proposed transition period optimization method has the advantage that the user need not specify minimum and maximum cycle length to achieve optimization, as is the case with current methods. Simulation results for three co‐ordinated intersections showed that the proposed method reduces total vehicle delay when compared to the ‘immediate’ transition method embedded in CORSIM traffic simulation software. This is due to the fact that vehicles on the minor street approaches get proportional green time without significantly affecting green times on the major street approach green phase. However, the method showed a slight increase in total delay for vehicles on the major street. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
11.
Lei Zhao Fu‐Quan Sun Jun‐Chao Ren Ben‐Wen Li 《Optimal control applications & methods.》2016,37(2):279-289
12.
Michael A. Patterson William W. Hager Anil V. Rao 《Optimal control applications & methods.》2015,36(4):398-421
A mesh refinement method is described for solving a continuous‐time optimal control problem using collocation at Legendre–Gauss–Radau points. The method allows for changes in both the number of mesh intervals and the degree of the approximating polynomial within a mesh interval. First, a relative error estimate is derived based on the difference between the Lagrange polynomial approximation of the state and a Legendre–Gauss–Radau quadrature integration of the dynamics within a mesh interval. The derived relative error estimate is then used to decide if the degree of the approximating polynomial within a mesh should be increased or if the mesh interval should be divided into subintervals. The degree of the approximating polynomial within a mesh interval is increased if the polynomial degree estimated by the method remains below a maximum allowable degree. Otherwise, the mesh interval is divided into subintervals. The process of refining the mesh is repeated until a specified relative error tolerance is met. Three examples highlight various features of the method and show that the approach is more computationally efficient and produces significantly smaller mesh sizes for a given accuracy tolerance when compared with fixed‐order methods. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
13.
This communication presents a spectral method for solving time-varying linear quadratic optimal control problems. Legendre–Gauss–Lobatto nodes are used to construct the mth-degree polynomial approximation of the state and control variables. The derivative x ·(t) of the state vector x (t) is approximaed by the analytic derivative of the corresponding interpolating polynomial. The performance index approximation is based on Gauss–Lobatto integration. The optimal control problem is then transformed into a linear programming problem. The proposed technique is easy to implement, efficient and yields accurate results. Numerical examples are included and a comparison is made with an existing result. 相似文献
14.
A linear optimization problem with unknown parameters from a given finite set is tackled. The problem is to find the robust time‐optimal control transferring a given initial point to a convex terminal compact set M for all unknown parameters in a shortest time. The robust maximum principle for this minimax problem is formulated. It gives a necessary and sufficient condition of robust optimality. Under natural conditions, the existence and uniqueness of robust optimal controls are proven when the resource set is a convex polytope. Several illustrating examples, including a bang–bang robust optimal control, are considered in detail. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
15.
Steven M. Ross Richard G. Cobb William P. Baker Frederick G. Harmon 《Optimal control applications & methods.》2015,36(2):198-217
Modern computational power and efficient direct collocation techniques are decreasing the solution time required for the optimal control problem, making real‐time optimal control (RTOC) feasible for modern systems. Current trends in the literature indicate that many authors are applying RTOC with a recursive open‐loop structure, relying on a high recursion rate for implicit state feedback to counter disturbances and other unmodeled effects without explicit closed‐loop control. The limitations of using rapid, instantaneous optimal solutions are demonstrated analytically and through application to a surface‐to‐air missile avoidance control system. Two methods are proposed for control structure implementation when using RTOC to take advantage of error integration through either classical feedback or disturbance estimation. Published 2014. This article is a U.S. Government work and is in the public domain in the USA. 相似文献
16.
In this study, we investigate the optimal control of a class of singularly perturbed linear stochastic systems with Markovian jumping parameters. After establishing an asymptotic structure for the stabilizing solution of the coupled stochastic algebraic Riccati equations, a parameter‐independent composite controller is derived. Furthermore, the cost degradation in a reduced‐order controller is discussed. Thus, the exactness of the proposed approximate control is discussed for the first time. As an additional important contribution, a numerical algorithm for solving the coupled stochastic algebraic Riccati equations is proposed, and the feature of the resulting higher‐order controller is shown. Finally, a simple example is presented to demonstrate the validity of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
17.
This paper studies a partially observed time‐inconsistent stochastic linear‐quadratic control system, in which the state follows a stochastic differential equation driven by a Brownian motion and an independent Poisson random measure. The cost functional contains a state‐dependent term and a quadratic term of the conditional expected state process, which will cause the time inconsistency in dynamic systems. By virtue of a classical spike variation approach, we define an equilibrium and derive a sufficient condition for the equilibrium in the fully observed system with stochastic coefficients. Then, we obtain the equilibrium with an explicit feedback form in deterministic coefficients case and discuss the existence and uniqueness of the solution of corresponding Riccati equations. Furthermore, we get filtering equations of the partially observed system and get the explicit equilibrium in some special case. 相似文献
18.
It is commonly believed that reduced‐order observers, including reduced‐order Kalman filters, cannot be used in the loop transfer recovery (LTR) design of the plant output side. In contrast to common understanding, we show that, at least for nonminimum‐phase plants, the reduced‐order Kalman filter can be used in the linear‐quadratic‐Gaussian (LQG)/LTR design of the plant output side with clear meaning in systems theory. The key concept is to regard a reduced‐order Kalman filter as a high‐gain full‐order Kalman filter. For the reduced‐order LQG controller, we examine the asymptotic property achieved by applying the recovery procedure used in the full‐order LQG/LTR design. Using the equivalent full‐order Kalman filter, we find that the sensitivity property of the reduced‐order LQG controller is asymptotically equivalent to that of a high‐gain partial output injection system. Motivated by this result, we propose the reduced‐order LQG/LTR procedure taking the high‐gain partial output injection system as a target. Some target properties are discussed to clarify the difference from the full‐order design. A multivariable design example is presented to show that the procedure provides a systematic design of a reduced‐order controller with optimality consideration. 相似文献
19.
While system dynamics are usually derived in continuous time, respective model‐based optimal control problems can only be solved numerically, ie, as discrete‐time approximations. Thus, the performance of control methods depends on the choice of numerical integration scheme. In this paper, we present a first‐order discretization of linear quadratic optimal control problems for mechanical systems that is structure preserving and hence preferable to standard methods. Our approach is based on symplectic integration schemes and thereby inherits structure from the original continuous‐time problem. Starting from a symplectic discretization of the system dynamics, modified discrete‐time Riccati equations are derived, which preserve the Hamiltonian structure of optimal control problems in addition to the mechanical structure of the control system. The method is extended to optimal tracking problems for nonlinear mechanical systems and evaluated in several numerical examples. Compared to standard discretization, it improves the approximation quality by orders of magnitude. This enables low‐bandwidth control and sensing in real‐time autonomous control applications. 相似文献
20.
Markus Rein Jan Mohring Tobias Damm Axel Klar 《Optimal control applications & methods.》2020,41(4):1352-1370