Hierarchical Control Problem Research Articles

Hierarchical Stackelberg Control for a Two-Stroke Linear System in Population Dynamics

We study a unique hierarchical control problem for a two-stoke linear system, adjoint to an age and space dependent population dynamics problem. Using Stackelberg's method, we introduce two levels of control: a boundary control to achieve optimal flow regulation and a distributed control for null controllability. Our approach employs Carleman inequalities to address non-homogeneous Dirichlet boundary conditions, leading to new insights in controlling invasive species populations. These results highlight the applicability of hierarchical controls in ecological systems, providing a robust framework for future studies in control theory and population dynamics.

ADP-based online compensation hierarchical sliding-mode control for partially unknown switched nonlinear systems with actuator failures

This article investigates an adaptive dynamic programming-based online compensation hierarchical sliding-mode control problem for a class of partially unknown switched nonlinear systems with actuator failures and uncertain perturbations under an identifier-critic neural networks architecture. Firstly, by introducing a cost function related to hierarchical sliding-mode surfaces for the nominal system, the original control problem is equivalently converted into an optimal control problem. To obtain this optimal control policy, the Hamilton–Jacobi–Bellman equation is solved through an adaptive dynamic programming method. Compared with conventional adaptive dynamic programming methods, the identifier-critic network architecture not only overcomes the limitation on the unknown internal dynamic but also eliminates the approximation error arising from the actor network. The weights in the critic network are tuned via the gradient descent approach and the experience replay technology, such that the persistence of excitation condition can be relaxed. Then, a compensation term containing hierarchical sliding-mode surfaces is used to offset uncertain actuator failures without the fault detection and isolation unit. Based on the Lyapunov stability theory, all states of the closed-loop nonlinear system are stable in the sense of uniformly ultimately boundedness. Finally, numerical and practical examples are given to demonstrate the effectiveness of our presented online compensation control strategy.

Hierarchical control problem for the heat equation with dynamic boundary conditions

Abstract This paper deals with a hierarchical control problem for the heat equation with dynamic boundary conditions. The main goal consists of letting the state near from a prescribed target in a fixed observation region. The secondary objective is the null controllability. In other words, we reverse the roles of the leader and the follower addressed in the recent article. For this purpose, we combine some appropriate Carleman estimates and the Stackelberg strategy. We also extend our study for hierarchical-biobjective problems by applying the Stackelberg–Pareto strategy.

Hierarchical Control for the Oldroyd Equation in Memoriam to Professor Luiz Adauto Medeiros.

This manuscript deals with a hierarchical control problem for Oldroyd equation under the Stackelberg-Nash strategy. The Oldroyd equation model is defined by non-regular coefficients, that is, they are bounded measurable functions. We assume that we can act in the dynamic of the system by a hierarchy of controls, where one main control (the leader) and several additional secondary control (the followers) act in order to accomplish their given tasks: controllability for the leader and optimization for followers. We obtain the existence and uniqueness of Nash equilibrium and its characterization, the approximate controllability with respect to the leader control, and the optimality system for leader control.

Enhancing dynamic operation optimization feasibility for constrained economic model predictive control systems

AbstractBased on the hierarchical control structure, optimization and control problems of large‐scale and multivariate plants are solved sequentially. The economic performance of the plant plays an essential role in the plant‐wide modern industry. The optimal operating conditions will change as the economic criteria changes throughout the operation of the plant as the result of variations in raw material prices, product prices, production demand, market fluctuations, disturbances, and so forth. In reality, soft constraints are frequently used to denote the production requirements of various operating conditions. In order to improve economic performance and guarantee feasibility for the entire plant operation, a novel economic model predictive control (EMPC) strategy is proposed to control the constrained multi‐variable process system with varying economic performance criteria under soft constraints. By incorporating the transient steady‐state and two categories of slack variables for soft constraints, a modified economic performance index is optimized to cope with the changing criteria. In addition, a contractive constraint is added to the closed‐loop system to guarantee stability for non‐dissipative stage costs. This approach ensures recursive feasibility and asymptotic stability. The effectiveness of the proposed method is demonstrated by numerical examples and the fluid catalytic cracking unit (FCCU) process.

A three-layer hierarchical model-based approach for network-wide traffic signal control

This paper introduces a three-layer hierarchical model-based approach for network-wide traffic signal control, which consists of a region coordination layer, an intersection coordination layer and a local signal control layer. The hierarchical control problem is formulated by two model predictive control (MPC) schemes. The upper-level control deals with the region coordination problem, which considers the cycle length optimization for different regions based on the macroscopic fundamental diagram. Under the guidance of the upper level MPC, a distributed MPC is developed to address both the green split optimization at each local intersection and the intersection coordination. For computational efficiency, the network is decomposed into separated intersections while the Lagrangian algorithm is developed for intersection coordination. Experimental results on the Nguyen-Dupuis network prove that our proposed three-layer hierarchical control approach has great potential in reducing the computational complexity while maintaining the overall performance (such as total travel time) of the traffic network.

Hierarchical MPC for a dynamic process system employing parametric global optimization strategy

The hierarchical decision making in process industries has been traditionally viewed as having a common objective, such as the overall cost, which needs to be optimized. However, a more appropriate approach is to formulate and solve hierarchical optimization and control problems. The solution algorithms for hierarchical optimization problems have been reported in the literature. The idea is to recast each optimization sub-problem in the hierarchy into a multiparametric programming problem, considering the variables of upper-level problems as unknown parameters. In this paper, explicit Model Predictive Control (MPC) and hierarchical optimization techniques, employing multiparametric programming, are combined for hierarchical MPC. The solution algorithm for hierarchical MPC is described in detail. Note that the solution to a hierarchical MPC problem is challenging, even for the simplest case of linear-quadratic objectives. Closed-loop simulations of a thermal mixing process, under two different hierarchical MPC formulations, are performed and the control performance is studied.

Off-policy algorithm based Hierarchical optimal control for completely unknown dynamic systems

This paper proposes an online reinforcement learning(RL) for solving Stackelberg games with completely unknown dynamic systems. To deal with the hierarchical optimal control problem, the key is to find the solution of a two-level optimal control with the leader’s optimal problem being constrained. Firstly, the leader–follower coupled Hamiltonian-Jacobi(HJ) equations subject to the follower’s costate equation is derived. Secondly, an off-policy scheme is designed following the policy iteration(PI) algorithm based on model. The improved off-policy algorithm is given for obtaining the solution to the leader–follower coupled HJ equations. The algorithm is built without requiring any knowledge of the dynamic system, and the leader–follower optimal control policies are directly constructed by the extracted data. Meanwhile, the existence of the Stackelberg equilibrium is demonstrated. Lastly, NNs for each player are built, and NN learning is accomplished online with Kronecker product technique and vectorization, which simples the NN form and could decrease computation burden. Simulation examples are presented to demonstrate the proposed learning algorithm.

Chapter 9 - Hierarchical cognitive control and the frontal lobes

Cognitive control refers to our ability to choose courses of thought and action that achieve our goals over habitual but contextually inappropriate ones. Hierarchical control problems are those in which multiple goals or contextual contingency must be managed at once and related to one another. In the open-ended complexity of the real world, hierarchical control arguably characterizes most of the problems faced by our control systems. And, it is these cases of hierarchical control where patients with damage to executive systems are most apt to fail, even those that perform well on simplified laboratory tasks. In this chapter, we consider the functional organization of frontal brain systems that support hierarchical cognitive control. We focus on two particular cases of hierarchical control. First, we discuss a line of work testing how managing multiple contingencies en route to a response relates to processing along the rostrocaudal axis of frontal cortex. Second, we consider cases of sequential tasks that require monitoring and behaving according to a series of tasks performed in time. In this latter case, we focus on the particular role of rostrolateral prefrontal cortex. We conclude with considerations of future directions of basic and clinically relevant research in this domain.

Stackelberg–Nash exact controllability for the Kuramoto–Sivashinsky equation

This paper deals with a hierarchical control problem for the Kuramoto–Sivashinsky equation following a Stackelberg–Nash strategy. We assume that there is a main control, called the leader, and two secondary controls, called the followers. The leader tries to drive the solution to a prescribed target and the followers intend to be a Nash equilibrium for given functionals. It is known that this problem is equivalent to a null controllability result for an optimality system consisting of three non-linear equations. One of the novelties is a new Carleman estimate for a fourth-order equation with right-hand sides in Sobolev spaces of negative order, which allows to relax some geometric conditions for the observation sets for the followers.

Distillation Column Hierarchical Control

This paper treats the problem of hierarchical control of a butylene-butane distillation column (BBDC). A hierarchical control system with three levels is proposed for BBDC. First hierarchical level, which is represented by the column with its conventional automation, is simulated and the results led to the idea of using a decoupler for the process crossed channels. Thus, it is proposed a nonlinear decoupler which determines automatically its parameters and type. At the second hierarchical level are implemented two internal model controllers for the top and bottom concentrations. Finally, the third hierarchical level consists of an optimal control system for the butylene-butane separation process.

Output feedback hierarchical control for nonlinear systems

SummaryIn this paper, we address the problem of hierarchical control for nonlinear systems and design two dynamic output feedback hierarchical control laws in a semiglobal sense and in a global sense, respectively. With the controllers applied to a class of nonlinear systems, some transient and steady properties of the system output trajectories can be satisfied simultaneously. Furthermore, the corresponding result in the global sense for linear systems is naturally derived. Finally, the effectiveness of our approach is illustrated by a single‐link robot arm system. Copyright © 2017 John Wiley & Sons, Ltd.

Hierarchical control for nonlinear systems by partial-state feedback

In this paper, the hierarchical control problem is rephrased and addressed that systematically tackles the design of hierarchical control law between the concrete system and the abstract system. The proposed way to this problem, on one hand, incorporates simulation function technique, and on the other hand, allows us to design a partial-state feedback hierarchical control law. Following this approach, we design two hierarchical control laws for nonlinear systems. Finally, an example illustrates this approach.

Adaptive hierarchical control for output feedback systems

ABSTRACTIn this paper, we address the problem of adaptive hierarchical control for a class of so-called uncertain output feedback systems. The proposed approach is to design an adaptive output interface dynamic by estimating the uncertainties. With the interface connected to the uncertain nonlinear system and a linear abstract system, the system could track approximately the abstraction. Finally, two examples are presented to illustrate our approach.

Robust output feedback hierarchical control for a class of non‐linear systems

In this study, the authors address the problem of robust output feedback hierarchical control for a class of uncertain non-linear systems. The proposed approach is to design an output interface dynamic which is connected to the non-linear system and a linear abstract system. In order to deal with the uncertainties, they resort to the notion of internal model from output regulation. Finally, the unknown point mass system illustrates their approach.

Hierarchical Control of Linear Systems from the Abstraction Feedback Gain

AbstractIn this paper, the problem of hierarchical control for a class of linear systems is addressed. Given a large‐scale linear system, we obtain a stabilizing feedback gain for it from that of an abstract system. And then, we employ this feedback gain to design a new interface between the original system and the abstraction. Furthermore, the synthesis of the new interface can be allowed by a new simulation function characterized by a low‐order matrix associated to the abstraction. Finally, an example is given to illustrate the proposed approach.

Hierarchical Topology Control and Routing Problem in Cluster-Based Wireless Sensor Networks

Hierarchical Topology Control and Routing Problem in Cluster-Based Wireless Sensor Networks

Dynamics of heterogeneity in urban networks: aggregated traffic modeling and hierarchical control

Real traffic data and simulation analysis reveal that for some urban networks a well-defined Macroscopic Fundamental Diagram (MFD) exists, which provides a unimodal and low-scatter relationship between the network vehicle density and outflow. Recent studies demonstrate that link density heterogeneity plays a significant role in the shape and scatter level of MFD and can cause hysteresis loops that influence the network performance. Evidently, a more homogeneous network in terms of link density can result in higher network outflow, which implies a network performance improvement. In this article, we introduce two aggregated models, region- and subregion-based MFDs, to study the dynamics of heterogeneity and how they can affect the accuracy scatter and hysteresis of a multi-subregion MFD model. We also introduce a hierarchical perimeter flow control problem by integrating the MFD heterogeneous modeling. The perimeter flow controllers operate on the border between urban regions, and manipulate the percentages of flows that transfer between the regions such that the network delay is minimized and the distribution of congestion is more homogeneous. The first level of the hierarchical control problem can be solved by a model predictive control approach, where the prediction model is the aggregated parsimonious region-based MFD and the plant (reality) is formulated by the subregion-based MFDs, which is a more detailed model. At the lower level, a feedback controller of the hierarchical structure, tries to maximize the outflow of critical regions, by increasing their homogeneity. With inputs that can be observed with existing monitoring techniques and without the need for detailed traffic state information, the proposed framework succeeds to increase network flows and decrease the hysteresis loop of the MFD. Comparison with existing perimeter controllers without considering the more advanced heterogeneity modeling of MFD highlights the importance of such approach for traffic modeling and control.

Hierarchical cooperative control for multiagent systems with switching directed topologies.

The hierarchical cooperative control problem is concerned for a two-layer networked multiagent system under switching directed topologies. The group cooperative objective is to achieve finite-time formation control for the upper layer of leaders and containment control for the lower layer of followers. Two kinds of cooperative strategies, including centralized-distributed control and distributed-distributed control, are proposed for two types of switching laws: 1) random switching law with the dwell time and 2) Markov switching law with stationary distribution. Utilizing the state transition matrix methods and matrix measure techniques, some sufficient conditions are derived for asymptotical containment control and exponential almost sure containment control, respectively. Finally, some numerical examples are provided to demonstrate the effectiveness of the proposed control schemes.

Disturbance‐observer‐based control & ℋ ∞ control for non‐linear Markovian jump singular systems with multiple disturbances

This study addresses the Problem of composite hierarchical anti-disturbance control [disturbance-observer-based controllers (DOBC) and ℋ∞ control] for Markovian jump singular systems with non-linearity and two types of disturbances (the first is generated by an exogenous system and the latter is norm-bounded). The authors’ attention is focused on the design of a disturbance observer to estimate the first disturbance, and then on constructing a composite hierarchical control scheme such that the solution to the composite system is unique and exists, the composite system can be guaranteed to be stochastically admissible, and different types of disturbances can be attenuated and rejected simultaneously. By constructing a proper stochastic Lyapunov–Krasovskii functional, sufficient conditions for the existence of the desired DOBCs are established. Finally, a numerical eEEExample is provided to show the effectiveness of the proposed approaches.