Fast reference governors for second-order linear systems with constraints and an input time-delay

This note provides a solution to the constrained command tracking problem using reference governors for a class of continuous-time second order linear systems with an input delay and with pointwise-in-time state and control constraints. The reference governor modifies the command to a closed-loop system based on the prediction of whether the system response to constant commands violates the specified constraints. The solution relies on classical control results for second order linear systems and requires only checking whether predicted outputs violate the constraints at a small number of time instants (e.g., four time instants in the single output case). This greatly simplifies the online computation, especially when a reference governor is applied to system models that are (slowly) changing in time. The effectiveness of the proposed method is demonstrated by a numerical example.     

Command governors for constrained nonlinear systems

A method is described for set-point tracking in nonlinear systems when pointwise-in-time input and/or state inequality constraints are to be enforced. It consists of adding to a primal compensated system a nonlinear device called command governor (CG) whose action is based on the current state, set-point, and prescribed constraints. The CG selects at any time the system input via a receding-horizon strategy from a virtual sequence amongst all possible command sequences by solving a constrained quadratic optimization problem. Provided that the initial state is admissible, the overall system is proved to fulfil the constraints and have desirable performance stability properties     

Nonlinear control of constrained linear systems via predictivereference management

A method based on conceptual tools of predictive control is described for solving set-point tracking problems wherein pointwise-in-time input and/or state inequality constraints are present. It consists of adding to a primal compensated system a nonlinear device, called command governor (CG), whose action is based on the current state, set-point, and prescribed constraints. The CG selects at any time a virtual sequence among a family of linearly parameterized command sequences, by solving a convex constrained quadratic optimization problem, and feeds the primal system according to a receding horizon control philosophy. The overall system is proved to fulfill the constraints, be asymptotically stable, and exhibit an offset-free tracking behavior, provided that an admissibility condition on the initial state is satisfied. Though the CG can be tailored for the application at hand by appropriately choosing the available design knobs, the required online computational load for the usual case of affine constraints is well tempered by the related relatively simple convex quadratic programming problem     

Generalized characterization of tracking systems and linear multivariable plants

In order to design tracking systems incorporating linear multivariable plants with more controlled outputs than manipulated inputs, it is shown that a more'general tracking concept than set-point tracking is necessary. The inclusion of inequalities in tracking conditions facilitates the characterization of tracking systems and linear multivariable plants. It is shown that the possibility of undertracking (i.e. tracking with non-negative errors) is characterized by the separation theorem of convex analysis, that linear multivariable plants can be classified into Class I and Class II plants based upon their steady-state transfer-function matrices, and that, in the case of Class I plants, undertracking is possible for any set-point commands. Furthermore, the necessary and/or sufficient conditions for Class I plants are given. Finally, it is shown that, in the case of Class 1 plants, undertracking is also possible for any set-point commands and any constant disturbances.     

Discrete-time reference governors and the nonlinear control of systems with state and control constraints

Discrete-time, linear control systems with specified pointwise-in-time constraints, such as those imposed by actuator saturation, are considered. The constraints are enforced by the addition of a nonlinear ‘reference governor’ that attenuates, when necessary, the input commands. Because the constraints are satisfied, the control system remains linear and undesirable response effects such as instability due to saturation are avoided. The nonlinear action of the reference governor is defined in terms of a finitely determined maximal output admissible set and can be implemented on-line for systems of moderately high order. The main result is global in nature: if the input command converges to a statically admissible input and the initial state of the system belongs to the maximal output admissible set, the eventual action of the reference governor is a unit delay.     

Reference governor for constrained piecewise affine systems

We present a methodology for designing reference tracking controllers for constrained, discrete-time piecewise affine systems. The approach follows the idea of reference governor techniques where the desired set-point is filtered by a system called the “reference governor”. Based on the system current state, set-point, and prescribed constraints, the reference governor computes a new set-point for a low-level controller so that the state and input constraints are satisfied and convergence to the original set-point is guaranteed.In this note we show how to design a reference governor for constrained piecewise affine systems by using polyhedral invariant sets, reachable sets, multiparametric programming and dynamic programming techniques.     

Nonlinear tracking control in the presence of state and control constraints: a generalized reference governor

This paper proposes a new approach to reference governor design. As in prior literature, the governor accepts input commands and modifies their evolution so that specified pointwise-in-time constraints on state and control variables are satisfied. The new approach applies to general discrete-time and continuous-time nonlinear systems with uncertainties. It relies on safety properties provided by sublevel sets of equilibria-parameterized functions. These functions need not be Lyapunov functions, and the corresponding sublevel sets need not be positively invariant. Technical conditions that capture the bare essentials of what is needed are identified and the usual desirable properties of reference governors are established. The new approach significantly broadens the class of methods available for constructing the nonlinear function that is required in the implementation of the reference governors. This advantage is illustrated in a nonlinear control problem where off-line, computer-based simulation is the basis for constructing the nonlinear function.     

Constrained linear systems with hard constraints and disturbances: An extended command governor with large domain of attraction

This paper considers a nonlinear feedback control policy that is an extension of those provided by command governors and reference governors. As in these control approaches it applies to discrete-time linear systems with hard constraints and set bounded disturbances. The control policy retains the main properties of traditional governors, such as straightforward direct implementation and finite-settling-time response to arbitrarily specified set points. Its principal advantage over traditional governors is a significantly larger domain of attraction, that may compete in size with those obtained by dynamic programming. Connections to model predictive control are made. Numerical examples illustrate advantageous features of the proposed approach.     

Robust command governors for constrained linear systems

Robust command governors are designed for discrete-time linear time-variant (LTV) systems with polytopic uncertainty models and subject to unknown bounded disturbances and pointwise-in-time input and state-related constraints.     

Robot motion command simplification and scaling

It has been observed that human limb motions are not very accurate, leading to the hypothesis that the human motor control system may have simplified motion commands at the expense of motion accuracy. Inspired by this hypothesis, we propose learning schemes that trade motion accuracy for motion command simplification. When the original complex motion commands capable of tracking motion accurately are reduced to simple forms, the simplified motion commands can then be stored and manipulated by using learning mechanisms with simple structures and scanty memory resources, and they can be executed quickly and smoothly. We also propose learning schemes that can perform motion command scaling, so that simplified motion commands can be provided for a number of similar motions of different movement distances and velocities without recalculating system dynamics. Simulations based on human motions are reported that demonstrate the effectiveness of the proposed learning schemes in implementing this accuracy-simplification tradeoff.     

并行扫描转换结构中的状态管理

扫描转换为图形流水线的核心部分,许多高性能的图形硬件都是采用并行的扫描转换结构。现代GPU(graphic processing unit)用于高性能计算时,主要依靠其极大的系统吞吐率,但是用基于传统的状态管理方法维持命令顺序性时会造成处理单元的停顿,降低系统的吞吐能力。提出一种新的状态管理方法,将命令分为计算与控制两类,对于控制类的命令由状态处理单元生成状态掩模(state-mask),减少了状态管理中的广播通信,降低了保持命令顺序性和状态管理的复杂性。仿真结果表明所提出状态管理方法同传统的状态管理方法相比,在游戏等后端状态变化明显的图形应用中,扫描引擎利用率提高了5%~9%。     

Design and stability discussion of an hybrid intelligent controller for an unordinary system

In this paper, the pitch angle control of a lab model helicopter is discussed. This problem has some specific features. As a major unusual feature, it is observed that the steady state control command is completely dependent on the setpoint, and for different setpoints, different steady state control commands are needed to keep the error around zero. Moreover, the system is one with highly oscillating dynamics. In order to solve this control problem, two controllers are designed: an artificial neural network (ANN), whose input is the setpoint, is used to provide steady state control command, and a fuzzy inference system (FIS), whose input is error, is used to provide transient control command. The total control command is the sum of the two aforementioned control commands. It is proven that both ANN and FIS are boundary‐input boundary‐output (BIBO) systems. Using this fact and considering two experimental assumptions, the closed‐loop stability is also proven. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Activation pattern controlled rules: Towards an integration of data-driven and command-driven programming

The attractions and drawbacks of data-driven programming are discussed in the context of rule-based forward chaining systems. The relationships between data-driven and command-driven programming are analyzed in the context of a course-registration example. A new form of production rule, called an activation pattern controlled rule, that generalizes classical forward chaining rules is introduced. Activation pattern controlled rules are triggered by calls of commands; that is, by the intension to perform a command but not necessarily by the result of applying the command itself. We demonstrate that activation pattern controlled rules facilitate the integration of data-driven and command-driven programming, support preventive programming as well, and allow for writing rule-based programs more transparently. We also survey our experiences in implementing an inference engine for activation pattern controlled rules.     

A distributed command governor based on graph colorability theory

In this paper, a distributed command governor (CG) strategy is introduced that, by the use of graph colorability theory, improves the scalability property and the performance of recently introduced distributed noncooperative sequential CG strategies. The latter are characterized by the fact that only 1 agent at a decision time is allowed to update its command, whereas all the others keep applying their previously computed commands. The scalability of these early CG distributed schemes and their performance are limited because the structure of the constraints is not taken into account in their implementation. Here, by exploiting the idea that agents that are not directly coupled by the constraints can simultaneously update their control actions, the agents in the network are grouped into particular subsets (turns). At each time instant, on the basis of a round‐robin policy, all agents belonging to a turn are allowed to update simultaneously their commands, whereas agents in other turns keep applying their previous commands. Then, a turn‐based distributed CG strategy is proposed and its main properties are analyzed. Graph colorability theory is used to determine the minimal number of turns and to distribute each agent in at least a turn. A novel graph colorability problem that allows one to maximize the frequency at which agents can update their commands is proposed and discussed. A final example is presented to illustrate the effectiveness of the proposed strategy.     

On Stability of Constrained Receding Horizon Control with Finite Terminal Weighting Matrix

In this paper, a new stabilizing receding horizon control, based on a finite input and state horizon cost with a finite terminal weighting matrix, is proposed for time-varying discrete linear systems with constraints. We propose matrix inequality conditions on the terminal weighting matrix under which closed-loop stability is guaranteed for both cases of unconstrained and constrained systems with input and state constraints. We show that such a terminal weighting matrix can be obtained by solving a linear matrix inequality (LMI). In the case of constrained time-invariant systems, an artificial invariant ellipsoid constraint is introduced in order to relax the conventional terminal equality constraint and to handle constraints. Using the invariant ellipsoid constraints, a feasibility condition of the optimization problem is presented and a region of attraction is characterized for constrained systems with the proposed receding horizon control.     

DAMN: a distributed architecture for mobile navigation

An architecture is presented in which distributed task-achieving modules, or behaviours, cooperatively determine a mobile robot's path by voting for each of various possible actions. An arbiter then performs command fusion and selects that action which best satisfies the prioritized goals of the system, as expressed by these votes, without the need to average commands. Command fusion allows multiple goals and constraints to be considered simultaneously. Examples of implemented systems are given, and future research directions in command fusion are discussed.     

Set-point Filter Design for a Two-degree-of-freedom Fractional Control System

This paper focuses on a new approach to design (possibly fractional) set-point filters for fractional control systems. After designing a smooth and monotonic desired output signal, the necessary command signal is obtained via fractional input-output inversion. Then, a set-point filter is determined based on the synthesized command signal. The filter is computed by minimizing the 2-norm of the difference between the command signal and the filter step response. The proposed methodology allows the designer to synthesize both integer and fractional setpoint filters. The pros and cons of both solutions are discussed in details. This approach is suitable for the design of two degreeof-freedom controllers capable to make the set-point tracking performance almost independent from the feedback part of the controller. Simulation results show the effectiveness of the proposed methodology.      

State feedback stabilization of cascaded nonlinear systems with discontinuous connection

In practical engineering, many phenomena are described as a discontinuous function of a state variable, and the discontinuity is usually the main reason for the degradation of the control performance. For example, in the set-point control problem of mechanical systems, the static friction （described by a sgn function of velocity of the contacting faces） causes undesired positioning error. In this paper, we will investigate the stabilization problem for a class of nonlinear systems that consist of two subsystems with cascaded connection. We will show the basic idea with a special case first, and then the result will be extended to more general cases. Some interesting numerical examples will be given to demonstrate the effectiveness of the proposed design approach.     

Fast reference governors for systems with state and control constraints and disturbance inputs

Reference governors are applied to closed-loop tracking systems that are linear and discrete time and have constraints on state and control variables. Earlier results are extended in significant ways. Disturbance inputs, whose values belong to a specified set, are allowed and a general class of reference governors is introduced. Each governor in the class guarantees constraint satisfaction for all reference and disturbance inputs. Moreover, if the reference input is ultimately confined to a neighbourhood of a constraint-admissible constant input, the eventual action of the reference governor reduces to a unit delay. By appropriately selecting reference governors from the allowed class it is possible to simplify significantly their implementation. The increase in on-line speed of operation overcomes prior limits on the practical application of reference governors. Algorithmic procedures are described which facilitate design of the reference governors. Several examples are presented. They illustrate the design process and the excellence of response to large inputs. Copyright © 1999 John Wiley & Sons, Ltd.     

A Smooth Wave‐Form Shaped Command with Flexible Maneuvering Time: Analysis and Experiments

Shaped commands are used to eliminate residual oscillations of crane payloads. Command jerks are detrimental to the safe and efficient operation of cranes. Smooth shaped commands are recommended to avoid such jerks in motion commands to crane motors. The amplitude of the shaped command is governed by its time length. The time length of the shaped command is highly dependent on the natural period of oscillation of the payload. A flexible time length of the shaped command introduces flexibility in selecting the desired command amplitude that would lead to a reduced stress on the crane actuators. In this work, a smooth wave‐form acceleration command is proposed to eliminate residual oscillations in rest‐to‐rest maneuvers of cranes. The proposed shaped command is derived analytically. The system performance is simulated numerically and validated experimentally on a scaled model of an overhead crane. The proposed wave‐form is further modified to relax the dependence of the profile on the natural period of oscillation of the payload.