Optimal preposterior observation of dynamic systems

Consideration was given to the problem of optimal observation which accompanies the problem of optimal control under multiple uncertainties using feedforward, feedback and combined, closable and closed, loops. Sets of the initial and current preposterior distributions of the terminal state of the dynamic system were introduced. Problems of linear programming were formulated to evaluate these sets. Positional solution of the optimal observation problem which may be used for positional solution of the optimal control problem under multiple uncertainties was established relying on the current preposterior distribution. A method of positional solution of the optimal observation problem using the optimal estimator which in real time generates the current values of the positional solution was proposed. The results obtained were illustrated by an example.     

Computational Method for a Class of Switched System Optimal Control Problems

We consider an optimal control problem with dynamics that switch between several subsystems of nonlinear differential equations. Each subsystem is assumed to satisfy a linear growth condition. Furthermore, each subsystem switch is accompanied by an instantaneous change in the state. These instantaneous changes-called ldquostate jumpsrdquo-are influenced by a set of control parameters that, together with the subsystem switching times, are decision variables to be selected optimally. We show that an approximate solution for this optimal control problem can be computed by solving a sequence of conventional dynamic optimization problems. Existing optimization techniques can be used to solve each problem in this sequence. A convergence result is also given to justify this approach.     

Domain decomposition and model reduction for the numerical solution of PDE constrained optimization problems with localized optimization variables

We introduce a technique for the dimension reduction of a class of PDE constrained optimization problems governed by linear time dependent advection diffusion equations for which the optimization variables are related to spatially localized quantities. Our approach uses domain decomposition applied to the optimality system to isolate the subsystem that explicitly depends on the optimization variables from the remaining linear optimality subsystem. We apply balanced truncation model reduction to the linear optimality subsystem. The resulting coupled reduced optimality system can be interpreted as the optimality system of a reduced optimization problem. We derive estimates for the error between the solution of the original optimization problem and the solution of the reduced problem. The approach is demonstrated numerically on an optimal control problem and on a shape optimization problem.     

火电供煤智能输配系统的研究与应用

针对火电厂现场煤粉输配需求,设计一种煤粉输配智能监控系统。系统按功能分为iFIX组态子系统、控制优化子系统、视频监控子系统和后台数据库管理子系统。分析配煤自动化的可编程逻辑控制、iFIX组态和优化控制过程,建立基于模糊决策的故障诊断和遗传算法的配煤和调度优化,采用VC++实现控制优化子系统功能以及各子系统间的通信。应用结果表明,该系统可实现煤粉输送控制自动化和优化混配智能化。     

Optimal control of system with continuous and discrete state variables

An optimization problem for a system composed of continuous and discrete subsystems is considered. The discrete subsystem is introduced to express a combinatorial constraint in conventional control problems. The objective, the state equation and the constraint are assumed linear. The problem is formulated as a mixed-integer linear program with a staircase structure. A feasible decomposition method is developed for obtaining a suboptimal solution to the problem. In applications to an optimal energy control and planning problem for a large-scale production plant, our method uses less computing time than the non-decomposition method.     

Optimal tracking control for nonlinear large-scale systems with persistent disturbances

This paper studies the optimal control with zero steady-state error problem for nonlinear large-scale systems affected by external persistent disturbances. The nonlinear large-scale system is transformed into N nonlinear subsystems with interconnect terms. Based on the internal model principle, a disturbance compensator is constructed such that the ith subsystem with external persistent disturbances is transformed into an augmented subsystem without disturbances. According to the sensitivity approach, the optimal tracking control law for the ith nonlinear subsystem can be obtained. The optimal tracking control law for the nonlinear large-scale systems can be obtained. A numerical simulation shows that the method is effective.     

Lossless convexification of a class of optimal control problems with non-convex control constraints

We consider a class of finite time horizon optimal control problems for continuous time linear systems with a convex cost, convex state constraints and non-convex control constraints. We propose a convex relaxation of the non-convex control constraints, and prove that the optimal solution of the relaxed problem is also an optimal solution for the original problem, which is referred to as the lossless convexification of the optimal control problem. The lossless convexification enables the use of interior point methods of convex optimization to obtain globally optimal solutions of the original non-convex optimal control problem. The solution approach is demonstrated on a number of planetary soft landing optimal control problems.     

Grid automata and supervisory control of dense real-time discrete event systems

We present a generalization of the classical supervisory control theory for discrete event systems to a setting of dense real-time systems modeled by Alur and Dill timed automata. The main problem involved is that in general the state space of a timed automaton is (uncountably) infinite. The solution is to reduce the dense time transition system to an appropriate finite discrete subautomaton, the grid automaton, which contains enough information to deal with the timed supervisory control problem (TSCP). The plant and the specifications region graphs are sampled for a granularity defined in a way that each state has an outgoing transition labeled with the same time amount. We redefine the controllability concept in the context of grid automata, and we provide necessary and sufficient solvability conditions under which the optimal solution to centralized supervisory control problems in timed discrete event systems under full observation can be obtained. The enhanced setting admits subsystem composition and the concept of forcible event. A simple example illustrates how the new method can be used to solve the TSCP.     

A hybrid model-based optimal control method for nonlinear systems using simultaneous dynamic optimization strategies

To improve the overall control performance of nonlinear systems, an optimal control method, based on the framework of hybrid systems, is proposed. Firstly, the nonlinear systems are approximated by a number of piecewise affine models which are produced by the nonlinear systems at the specified operating points, then the piecewise affine models are synthesized under the framework of hybrid systems, and an associated optimal control problem, in which decision variables involve not only admissible continuous control but also the scheduling of subsystem modes, is established. Secondly, the optimal control problem is transformed into a MIQP problem by discretization over the whole state space and admissible control space to obtain the numerical optimal solution. For speeding up the algorithm, the simultaneous method on finite elements is used to lower the dimensions of the MIQP problem. Consequently, a hybrid model-based MPC for nonlinear systems is designed, and the adverse effects of model mismatch resulted from simultaneous method is weakened by MPC strategy. Simulations and comparisons with soft-switching method, hard-switching method and MLD method, confirm that a satisfactory performance can be obtained using the presented approach.     

A new reduction technique for a class of singularly perturbedoptimal control problems

We consider a class of singularly perturbed optimal control problems which may not be approximated by the reduced problems constructed via the formal replacement of the fast variables by the states of equilibrium of the “fast” subsystem considered with “frozen” slow variables and controls. We construct a reduced optimal control problem which provides a true approximation for the problems under consideration and write down the necessary and sufficient optimality conditions for this reduced problem     

An integrated state space partition and optimal control method of multi-model for nonlinear systems based on hybrid systems

Multilinear model approach turns out to be an ideal candidate for dealing with nonlinear systems control problem. However, how to identify the optimal active state subspace of each linear subsystem is an open problem due to that the closed-loop performance of nonlinear systems interacts with these subspaces ranges. In this paper, a new systematic method of integrated state space partition and optimal control of multi-model for nonlinear systems based on hybrid systems is initially proposed, which can deal with the state space partition and associated optimal control simultaneously and guarantee an overall performance of nonlinear systems consequently. The proposed method is based on the framework of hybrid systems which synthesizes the multilinear model, produced by nonlinear systems, in a unified criterion and poses a two-level structure. At the upper level, the active state subspace of each linear subsystem is determined under the optimal control index of a hybrid system over infinite horizon, which is executed off-line. At the low level, the optimal control is implemented online via solving the optimal control of hybrid system over finite horizon. The finite horizon optimal control problem is numerically computed by simultaneous method for speeding up computation. Meanwhile, the model mismatch produced by simultaneous method is avoided by using the strategy of receding-horizon. Simulations on CSTR (Continuous Stirred Tank Reactor) confirm that a superior performance can be obtained by using the presented method.     

Constrained Optimal Hybrid Control of a Flow Shop System

We consider an optimal control problem for the hybrid model of a deterministic flow shop system, in which the jobs are processed in the order they arrive at the system. The problem is decomposed into a higher-level discrete-event system control problem of determining the optimal service times, and a set of lower-level classical control problems of determining the optimal control inputs for given service times. We focus on the higher-level problem which is nonconvex and nondifferentiable. The arrival times are known and the decision variables are the service times that are controllable within constraints. We present an equivalent convex optimization problem with linear constraints. Under some cost assumptions, we show that no waiting is observed on the optimal sample path. This property allows us to simplify the convex optimization problem by eliminating variables and constraints. We also prove, under an additional strict convexity assumption, the uniqueness of the optimal solution and propose two algorithms to decompose the simplified convex optimization problem into a set of smaller convex optimization problems. The effects of the simplification and the decomposition on the solution times are shown on an example problem.     

Maximal Lifetime Scheduling for Sensor Surveillance Systems with K Sensors to One Target

This paper addresses the maximal lifetime scheduling for sensor surveillance systems with K sensors to 1 target. Given a set of sensors and targets in an Euclidean plane, a sensor can watch only one target at a time and a target should be watched by k, k geq 1, sensors at any time. Our task is to schedule sensors to watch targets and pass data to the base station, such that the lifetime of the surveillance system is maximized, where the lifetime is the duration up to the time when there exists one target that cannot be watched by k sensors or data cannot be forwarded to the base station due to the depletion of energy of the sensor nodes. We propose an optimal solution to find the target watching schedule for sensors that achieves the maximal lifetime. Our solution consists of three steps: 1) computing the maximal lifetime of the surveillance system and a workload matrix by using linear programming techniques, 2) decomposing the workload matrix into a sequence of schedule matrices that can achieve the maximal lifetime, and 3) determining the sensor surveillance trees based on the above obtained schedule matrices, which specify the active sensors and the routes to pass sensed data to the base station. This is the first time in the literature that this scheduling problem of sensor surveillance systems has been formulated and the optimal solution has been found. We illustrate our optimal method by a numeric example and experiments in the end.     

Data-driven optimal switching and control of switched systems

In this paper, optimal switching and control approaches are investigated for switched systems with infinite-horizon cost functions and unknown continuous-time subsystems. At first, for switched systems with autonomous subsystems, the optimal solution based on the finite-horizon HJB equation is proposed and a data-driven optimal switching algorithm is designed. Then, for the switched systems with subsystem inputs, a data-driven optimal control approach based on the finite-horizon HJB equation is proposed. The data-driven approaches approximate the optimal solutions online by means of the system state data instead of the subsystem models. Moreover, the convergence of the two approaches is analyzed. Finally, the validity of the two approaches is demonstrated by simulation examples.     

A Parallel Computational Model for Heterogeneous Clusters

This paper addresses the maximal lifetime scheduling for sensor surveillance systems with K sensors to 1 target. Given a set of sensors and targets in an Euclidean plane, a sensor can watch only one target at a time and a target should be watched by k, kges1, sensors at any time. Our task is to schedule sensors to watch targets and pass data to the base station, such that the lifetime of the surveillance system is maximized, where the lifetime is the duration up to the time when there exists one target that cannot be watched by k sensors or data cannot be forwarded to the base station due to the depletion of energy of the sensor nodes. We propose an optimal solution to find the target watching schedule for sensors that achieves the maximal lifetime. Our solution consists of three steps: 1) computing the maximal lifetime of the surveillance system and a workload matrix by using linear programming techniques, 2) decomposing the workload matrix into a sequence of schedule matrices that can achieve the maximal lifetime, and 3) determining the sensor surveillance trees based on the above obtained schedule matrices, which specify the active sensors and the routes to pass sensed data to the base station. This is the first time in the literature that this scheduling problem of sensor surveillance systems has been formulated and the optimal solution has been found. We illustrate our optimal method by a numeric example and experiments in the end     

多学科协同优化算法的分析和改进

针对协同优化算法计算量大、优化结果多为局部最优解的问题,提出了一种改进的协同优化算法。首先,在系统级一致性等式约束中采用改进的松弛因子,使系统级优化的可行域是存在的,且可行域的范围逐步减小,以保证子学科间的一致性;其次,在子学科中,将目标函数分为一致性目标函数和子学科最优目标函数两个部分,以不同的权重相加作为子学科的目标函数,既考虑了一致性,又兼顾了子学科独立性。最后,以各子学科级独立优化结果作为初始点进行优化。采用两个经典案例对改进算法进行验证,优化结果表明,改进的算法具有更好收敛速度和可行性。     

Decentralized,stochastic control for a static LQ problem

An original problem statement for the optimal control laws design is presented. A large scale system composed of M linear static subsystems with an interaction and quadratic performance index is considered. A two-level hierarchical control structure is assumed, in which a coordinator and local controllers have access to different information. The so-called elastic constraint (Gessing 1985) is used for coordination. For the problem the possibility of partial decomposition of calculations and a decentralization of the control, as well as an analytical form of the optimal laws are obtained. The influence of the particular subsystem on the control quality is investigated.     

Linear–quadratic switching control with switching cost

We study in this paper the linear–quadratic (LQ) optimal control problem of discrete-time switched systems with a constant switching cost for both finite and infinite time horizons. We reduce these problems into an auxiliary problem, which is an LQ optimal switching control problem with a cardinality constraint on the total number of switchings. Based on the solution structure derived from the dynamic programming (DP) procedure, we develop a lower bounding scheme by exploiting the monotonicity of the Riccati difference equation. Integrating such a lower bounding scheme into a branch and bound (BnB) framework, we offer an efficient numerical solution scheme for the LQ switching control problem with switching cost.     

Distributed receding horizon control for multi-vehicle formation stabilization

We consider the control of interacting subsystems whose dynamics and constraints are decoupled, but whose state vectors are coupled non-separably in a single cost function of a finite horizon optimal control problem. For a given cost structure, we generate distributed optimal control problems for each subsystem and establish that a distributed receding horizon control implementation is stabilizing to a neighborhood of the objective state. The implementation requires synchronous updates and the exchange of the most recent optimal control trajectory between coupled subsystems prior to each update. The key requirements for stability are that each subsystem not deviate too far from the previous open-loop state trajectory, and that the receding horizon updates happen sufficiently fast. The venue of multi-vehicle formation stabilization is used to demonstrate the distributed implementation.