3D environmental extremum seeking navigation of a nonholonomic mobile robot

A nonholonomic under-actuated robot with bounded control travels in a 3D region. A single sensor provides the value of an unknown scalar field at the current location of the robot. We present a new kinematic control paradigm to drive the robot to the maximizer of the field, which is different from conventionally trying to align the velocity vector with the field gradient. The proposed strategy does not employ gradient estimation and is non-demanding with respect to both computation and motion. Its mathematically rigorous analysis and justification are provided. Simulation results confirm the applicability and performance of the proposed guidance approach.     

Distributed extremum seeking and formation control for nonholonomic mobile network

In this paper, an integrated control and optimization problem is studied in the context of formation and coverage of a cluster of nonholonomic mobile robots. In particular, each communication channel is modeled by its outage probability, and hence, connectivity is maintained if the outage probability is less than a certain threshold. The objective of the communication network is to not only maintain resilient communication quality but also extend the network coverage. An information theory based performance index is defined to quantify this control objective. Unlike most of the existing results, the proposed cooperative control design does not assume the knowledge of any gradient (of the performance index). Rather, a distributed extremum seeking algorithm is designed to optimize the connectivity and coverage of the mobile network. The proposed approach retains all the advantages of cooperative control, and it can not only perform extremum seeking individually, but also ensures a consensus of estimates between any pair of connected systems. Simulation results demonstrate effectiveness of the proposed methodology.     

An extremum seeking approach via variable-structure control for fed-batch bioreactors with uncertain growth rate

In this paper, we present an extremum-seeking scheme based on an approach to variable structure control for fed-batch bioreactors. The proposed scheme deals with uncertainty on the specific growth rate without assuming an explicit mathematical expression. The control approach exploits the inhibitory effect of the substrate concentration on the growth rate, in such a manner that the closed-loop system reaches the sliding regime on an optimal switching manifold, which is defined by maximizing biomass production. The control scheme comprises an estimation scheme consisting of a high-gain observer and a discrete gradient estimator which computes the unknown terms. The practical stabilizability for the closed-loop system around an unknown optimal set-point is analyzed. Numerical experiments illustrate the effectiveness of the proposed approach.     

极值搜索控制系统的一体化设计研究

针对传统极值搜索控制系统设计中,极值搜索算法与控制器采取单独设计易导致系统难以发挥其最佳性能的问题,提出一套极值搜索控制系统的一体化设计方法.此方法充分考虑到系统的非线性和不确定性,建立了极值搜索算法与被控对象的一体化设计模型,运用终端滑模切换面和相应的控制策略,使极值搜索算法在较短时间内搜寻到系统的最优值,而且其输出值可很快收敛至此最优值.理论分析和仿真结果分别验证了此方法的稳定性和有效性.     

Nonlinear control for reactive navigation of a nonholonomic robot for environmental nongradient‐based extremum seeking in maze‐like scenes

A single Dubins car‐like mobile robot travels with a constant speed in a planar workspace cluttered with arbitrarily complex obstacles, possibly maze‐like ones. An unknown scalar field is defined on the plane. The sensors supply the robot with the field value at its current location and its distance to the nearest obstacle. We present a new control law that drives the robot to the location where the field attains its maximum, while avoiding collisions with the obstacles. This is justified by a mathematically rigorous global convergence result and is confirmed via computer simulations. The proposed algorithm does not use gradient estimation and is nondemanding with respect to computation and motion. Copyright © 2017 John Wiley & Sons, Ltd.     

Extremum seeking with sliding mode gradient estimation and asymptotic regulation for a class of nonlinear systems

This paper presents a model-based extremum seeking approach for a class of single-input–single-output nonlinear systems, with the analytic form of the performance function unknown a priori. We focus on a practically implementable design with robustness to model uncertainties and disturbances. A discrete-time sliding mode gradient estimator is developed for estimating the gradient of the performance profile. Based on the estimate, a variable structure output feedback regulator is proposed to enforce the system states toward the optimal trajectory. We analyze convergence conditions of the switching system toward a neighborhood of the optimal trajectory, and establish an ultimate bound on the size of the neighborhood. The robustness of the proposed controller is discussed with respect to measurement noise.     

Robust adaptive control for a nonholonomic mobile robot with unknown parameters

A robust adaptive controller for a nonholonomic mobile robot with unknown kinematic and dynamic parameters is proposed. A kinematic controller whose output is the input of the relevant dynamic controller is provided by using the concept of backstepping. An adaptive algorithm is developed in the kinematic controller to approximate the unknown kinematic parameters, and a simple single-layer neural network is used to express the highly nonlinear robot dynamics in terms of the known and unknown parameters. In order to attenuate the effects of the uncertainties and disturbances on tracking performance, a sliding mode control term is added to the dynamic controller. In the deterministic design of feedback controllers for the uncertain dynamic systems, upper bounds on the norm of the uncertainties are an important clue to guarantee the stability of the closed-loop system. However, sometimes these upper bounds may not be easily obtained because of the complexity of the structure of the uncertainties. Thereby, simple adaptation laws are proposed to approximate upper bounds on the norm of the uncertainties to address this problem. The stability of the proposed control system is shown through the Lyapunov method. Lastly, a design example for a mobile robot with two actuated wheels is provided and the feasibility of the controller is demonstrated by numerical simulations.     

Navigation with constraints for an autonomous mobile robot

This paper describes a navigation planning algorithm for a robot capable of autonomous navigation in a structured, partially known and dynamic environment. This algorithm is applied to a discrete workspace composed of a network of places and roads. The environment specification associates temporal constraints with any element of the network, and recharge or relocalisation possibilities with places. A mission specification associates several constraints with each navigation task (energy, time, position uncertainty and distance).

The algorithm computes an optimal path for each navigation task according to the optimization criterion and constraints. We introduce the notion of efficient path applied to a new best first search algorithm solving a multiple constraints problem. The path determination relies on a state representation adapted to deal with environment constraints. We then prove that the complexity chracteristics of our algorithm are similar to those of the A* algorithm.

The planner described in this paper has been implemented on a Spare station for a Robuter mobile platform equipped with ultra-sonic range sensors and an active stereo vision system. It was developed for the MITHRA family of autonomous surveillance robots as part of project EUREKA EU 110.     

Range-only measurements based target following for wheeled mobile robots

We consider the problem of navigation and guidance of a wheeled mobile robot towards a maneuvering target based on the measurements concerning only the distance from the robot to the target. We propose a sliding mode controller that drives the robot to the predefined distance from the target and makes the robot follow the target at this distance. Mathematically rigorous proof of convergence and stability of the proposed guidance law is presented. Simulation results confirm the applicability and performance of the proposed guidance approach.     

Global output-feedback extremum seeking for a class of nonlinear dynamic systems with arbitrary relative degree

ABSTRACT

An output-feedback sliding-mode-based extremum-seeking controller was recently introduced for linear uncertain systems by using periodic switching functions. Nonlinear systems were also considered but restricted to relative degree one plants as well as the former linear case. Here, generalisation is achieved to include more general dynamics with arbitrary relative degree, thanks to the introduction of a high-gain adaptive observer with updated gain. Global stability properties of the closed-loop system with convergence to a controlled neighbourhood of the desired maximum point are also rigorously proved. Simulation and experimental results illustrate the performance of the proposed extremum-seeking control algorithm.     

On global extremum seeking in the presence of local extrema

We propose a global extremum seeking scheme which can seek the global optimal value in the presence of local extrema. It is shown that the proposed global extremum seeking scheme can converge to an arbitrarily small neighborhood of the global extremum from an arbitrarily large set of initial conditions if sufficient conditions are satisfied. A simple example illustrates the effectiveness of the proposed scheme.     

On-line optimization of fedbatch bioreactors by adaptive extremum seeking control

In this paper, we present an adaptive extremum seeking control scheme for fed-batch bioreactors with Haldane kinetics. The proposed adaptive extremum seeking approach utilizes the structure information of the process kinetics to derive a seeking algorithm that drives the system states to the desired setpoints that maximize the biomass production. It assumes that only the substrate concentration is available for on-line measurement. Lyapunov stability is used in the design of the extremum seeking controller structure and the development of the parameter learning laws. The performance of the approach is illustrated via numerical simulations.     

基于粒子群优化算法的极限环极值搜索控制

提出一种利用粒子群优化算法进行在线寻优的自适应控制算法,该方法可抑制极限环的振荡幅值．应用极值搜索控制的思想,在线测量极限环的振荡幅度,并将其作为优化目标,利用粒子群优化算法寻找最优控制量,使得极限环的振荡幅值最小．针对粒子群优化和极限环控制的特点,提出一种加快收敛的算法．数值实验表明,提出的算法不仅与传统基于摄动方法...     

On non-local stability properties of extremum seeking control

In this paper, we consider several extremum seeking schemes and show under appropriate conditions that these schemes achieve extremum seeking from an arbitrarily large domain of initial conditions if the parameters in the controller are appropriately adjusted. This non-local stability result is proved by showing semi-global practical stability of the closed-loop system with respect to the design parameters. We show that reducing the size of the parameters typically slows down the convergence rate of the extremum seeking controllers and enlarges the domain of the attraction. Our results provide guidelines on how to tune the controller parameters in order to achieve extremum seeking. Simulation examples illustrate our results.     

四旋翼无人机自适应导航控制

研究四旋翼(Quadrotor)无人机导航控制问题。针对传统的四旋翼无人机导航控制方法的目标定位误差和实时性差问题,提出了基于CLOS技术的导航控制方法。采用CLOS技术所开发的导航控制系统使得四旋翼无人机能够在移动停机坪完成自主导航和着陆的任务,并详细研究了导航控制系统的设计和仿真。仿真结果显示了所设计的导航控制系统的性能和有效性,可应用于四旋翼无人机的实时导航。     

Experimental evaluation of anti-windup extremum seeking control for airside economizers

The performance of anti-windup extremum seeking control (ESC) as a model free online optimization strategy is evaluated by experimental studies for energy efficient operation of both chilled-water and direct-expansion airside economizers. For the chilled-water based system, the ESC takes the chilled-water valve control signal as the feedback, and controls the outdoor air damper (OAD) position to minimize the cooling coil load. For the direct-expansion system, the ESC takes the total electricity power consumption as the feedback, and controls the OAD position to minimize the power consumption. Experimental results verify the effectiveness of the ESC scheme for model-free operation without temperature and humidity measurements.     

Almost sure convergence of extremum seeking algorithm using stochastic perturbation

This paper presents an extremum seeking (ES) algorithm where the perturbation signal is a martingale difference sequence (m.d.s.) with a vanishing variance. The measurement noise at the plant output is modeled by a superposition of deterministic component, and a non-stationary colored noise signal. The optimizing set point of the uncertain reference-to-output equilibrium map is estimated by a stochastic approximation (SA)-type algorithm. The algorithm has a vanishing gain sequence dependent on the set point estimates. By utilizing powerful tools of the martingale convergence theory it is proved that with probability one the set point estimates converge to the optimizing equilibrium point, in spite of the presence of a measurement noise. This result is derived without requiring boundedness or any prior condition on the set point estimates.     

Combining extremum seeking control and tracking control for high-performance CVT operation

The design of a new controller for the variator in a pushbelt continuously variable transmission (CVT) is investigated. A conventional variator controller is typically based on a variator model with large uncertainties, which results in a limited variator efficiency. The proposed controller simultaneously optimizes the variator efficiency and tracks a transmission ratio reference, for which a detailed variator model is not required. The controller, a combination of extremum seeking control and tracking control, only uses measurements from standard sensors. Experiments on the basis of a driving cycle show that a conventional variator controller is outperformed.     

Robust and adaptive design of numerical optimization-based extremum seeking control

We consider the employment of numerical optimization and state regulation to solve the extremum seeking control (ESC) problem, which does not assume the time scale separation between the plant dynamics and the extremum seeking loop. Extremum seeking is realized via a state regulator that drives the state traveling along a convergent set point sequence generated by a numerical optimization algorithm. In this paper, we propose a novel design of an asymptotic state regulator via output tracking for state feedback linearizable systems, where we trade off finite time state regulation to obtain flexibility in designing a robust extremum seeking controller. Existing techniques such as nonlinear damping and nonlinear adaptive control are then used to deal with input disturbance and unmodeled plant dynamics. Simulation examples illustrate the effectiveness of the basic and robust extremum seeking schemes, and some design guidelines are provided for engineering applications.