State estimation and nonlinear predictive control of autonomous hybrid system using derivative free state estimators

In this work, we develop a state estimation scheme for nonlinear autonomous hybrid systems, which are subjected to stochastic state disturbances and measurement noise, using derivative free state estimators. In particular, we propose the use of ensemble Kalman filters (EnKF), which belong to the class of particle filters, and unscented Kalman filters (UKF) to carry out estimation of state variables of autonomous hybrid system. We then proceed to develop novel nonlinear model predictive control (NMPC) schemes using these derivative free estimators for better control of autonomous hybrid systems. A salient feature of the proposed NMPC schemes is that the future trajectory predictions are based on stochastic simulations, which explicitly account for the uncertainty in predictions arising from the uncertainties in the initial state and the unmeasured disturbances. The efficacy of the proposed state estimation based control scheme is demonstrated by conducting simulation studies on a benchmark three-tank hybrid system. Analysis of the simulation results reveals that EnKF and UKF based NMPC strategies is well suited for effective control of nonlinear autonomous three-tank hybrid system.     

Robust fault isolation for a class of non-linear input?output systems

The design and analysis of fault diagnosis methodologies for non-linear systems has received significant attention recently. This paper presents a robust fault isolation scheme for a class of non-linear systems with unstructured modelling uncertainty and partial state measurement. The proposed fault diagnosis architecture consists of a fault detection and approximation estimator and a bank of isolation estimators. Each isolation estimator corresponds to a particular type of fault in the fault class. A fault isolation decision scheme is presented with guaranteed performance. If at least one component of the output estimation error of a particular fault isolation estimator exceeds the corresponding adaptive threshold at some finite time, then the occurrence of that type of fault can be excluded. Fault isolation is achieved if this is valid for all but one isolation estimator. Based on the class of non-linear systems under consideration, fault isolability conditions are rigorously investigated, characterizing the class of non-linear faults that are isolable by the proposed scheme. Moreover, the non-conservativeness of the fault isolability conditions is illustrated by deriving a subclass of nonlinear systems and faults for which this condition is also necessary for fault isolability. A simulation example of a simple robotic system is used to show the effectiveness of the robust fault isolation methodology.     

一类不确定脉冲型混杂系统的保代价控制

针对混合代价函数,研究了参数不确定脉冲型混杂系统的保代价控制问题,给出了混杂状态反馈保代价控制律的设计方法,由此得到的控制律既能使系统闭环鲁棒渐近稳定,又可使系统的闭环混合代价指标在对象参数摄动的范围内不超过确定的上界.本文提出的控制律不仅包含连续时间动态,也包含离散事件动态,而且其离散事件动态行为不需要与被控系统的离散事件动态行为一致,因此设计时不要求被控系统的每个连续时间子系统都具有可控性.仿真结果表明所提设计方法是可行有效的.     

Fault-tolerant control for a class of non-linear systems with dead-zone

In this paper, a fault-tolerant control scheme is proposed for a class of single-input and single-output non-linear systems with the unknown time-varying system fault and the dead-zone. The non-linear state observer is designed for the non-linear system using differential mean value theorem, and the non-linear fault estimator that estimates the unknown time-varying system fault is developed. On the basis of the designed fault estimator, the observer-based fault-tolerant tracking control is then developed using the backstepping technique for non-linear systems with the dead-zone. The stability of the whole closed-loop system is rigorously proved via Lyapunov analysis and the satisfactory tracking control performance is guaranteed in the presence of the unknown time-varying system fault and the dead-zone. Numerical simulation results are presented to illustrate the effectiveness of the proposed backstepping fault-tolerant control scheme for non-linear systems.     

A fault-tolerant control strategy for non-linear discrete-time systems: application to the twin-rotor system

In this paper, an active fault-tolerant control scheme is proposed in the case of actuator faults. In particular, the general idea of integrating fault identification and control schemes, which takes into account the fault estimation error is first presented in a linear context. As a result, the so-called separation principle for the controller and the fault identification scheme is developed. Subsequently, the proposed approach is extended to a class of non-linear systems. Similarly to the linear case, it is proven that using a suitable control strategy and a faulty identification scheme it is possible to obtain an integrated fault-tolerant control framework, which takes into account the fault identification error. As a result, a non-linear counterpart of the above-mentioned separation principle is developed. Finally, the last part of the paper shows the application results obtained using a twin-rotor system that confirm the high performance of the proposed approach.     

Robust MPC for systems with output feedback and input saturation

In this work, it is proposed an MPC control algorithm with proved robust stability for systems with model uncertainty and output feedback. It is assumed that the operating strategy is such that system inputs may become saturated at transient or steady state. The developed strategy aims at the case in which the controller performs in the output-tracking scheme following an optimal set point that is provided by an upper optimization layer of the plant control structure. In this case, the optimal operating point usually lies at the boundary of the region where the input is defined. Assuming that the system remains stabilizable in the presence of input saturation, the design of the robust controller is performed off-line and an on-line implementation strategy is proposed. At each sampling step, a sub optimal control law is obtained by combining control configurations that correspond to particular subsets of available manipulated inputs. Stability of the closed-loop system is forced by considering in the off-line step of the controller design, a state contracting restriction for the closed-loop system. To produce an offset free controller and to attend the case of unknown steady state, the method is developed for a state-space model in the incremental form. The method is illustrated with simulation examples extracted from the process industry.     

Path-following with a bounded-curvature vehicle: a hybrid control approach

In this paper, we consider the problem of stabilizing the kinematic model of a car to a path in the plane under rather general conditions. The path is subject to very mild restrictions, while the car model, although rather simplified, contains the most relevant limitations inherent in wheeled robots kinematics. Namely, the car can only move forward, its steering radius is lower bounded and a limited sensory information only provides a partial knowledge of some state parameters. In particular, we consider the case that the current distance and the heading angle error with respect to the closest point on the reference path can be measured but only the sign of the path curvature is detected. These constraints are such to make classical control techniques inefficient. As the feedback information is both continuous and discrete, the hybrid systems formalism turns out to be well appropriate to model the problem. The proposed approach is based on optimal control techniques successfully applied in a previous work for following rectilinear paths. We propose here an extension to the tracking of more general paths with moderate curvature. The stability of the closed-loop system is proved by means of hybrid system formalisms and hybrid formal verification techniques. Finally, the practicality of the proposed approach, in spite of non-idealities in real-world applications, is discussed by reporting experimental results.     

MPEC strategies for optimization of a class of hybrid dynamic systems

With the development and widespread use of large-scale nonlinear programming (NLP) tools for process optimization, there has been an associated application of NLP formulations with complementarity constraints in order to represent discrete decisions. In particular, these constraints arise frequently in equation-based formulations for real-time optimization. Also known as mathematical programs with equilibrium constraints (MPECs), these formulations can be used to model certain classes of discrete events and can be more efficient than a mixed integer formulation, particularly for large systems with many discrete decisions, such as dynamic systems with switches at any point in time. In this study, we consider and extend MPEC formulations for the optimization of a class of hybrid dynamic models, where the differential states remain continuous over time. These include differential inclusions of the Filippov type. Here, particular care is required in the formulation in order to preserve smoothness properties of the dynamic system. Results on three case studies, including process control examples, illustrate the effectiveness and accuracy of the proposed MPEC optimization methodology for a class of hybrid dynamic systems.     

Non-linear dynamics of flexible multibody systems

In this work we set to examine several important issues pertinent to currently very active research area of the finite element modeling of flexible multibody system dynamics. To that end, we first briefly introduce three different model problems in non-linear dynamics of flexible 3D solid, a rigid body and 3D geometrically exact beam, which covers the vast majority of representative models for the particular components of a multibody system. The finite element semi-discretization for these models is presented along with the time-discretization performed by the mid-point scheme. In extending the proposed methodology to modeling of flexible multibody systems, we also present how to build a systematic representation of any kind of joint connecting two multibody components, a typical case of holonomic contraint, as a linear superposition of elementary constraints. We also indicate by a chosen model of rolling contact, an example of non-holonomic constraint, that the latter can also be included within the proposed framework. An important aspect regarding the reduction of computational cost while retaining the consistency of the model is also addressed in terms of systematic use of the rigid component hypothesis, mass lumping and the appropriate application of the explicit-implicit time-integration scheme to the problem on hand. Several numerical simulations dealing with non-linear dynamics of flexible multibody systems undergoing large overall motion are presented to further illustrate the potential of presented methodology. Closing remarks are given to summarize the recent achievements and point out several directions for future research.     

A systematic method to obtain ultimate bounds for perturbed systems

In this paper, we develop a systematic method to obtain ultimate bounds for both continuous- and discrete-time perturbed systems. The method is based on a componentwise analysis of the system in modal coordinates and thus exploits the system geometry as well as the perturbation structure without requiring calculation of a Lyapunov function for the system. The method is introduced for linear systems having constant componentwise perturbation bounds and is then extended to the case of state-dependent perturbation bounds. This extension enables the method to be applied to non-linear systems by treating the perturbed non-linear system as a linear system with a perturbation bounded by a non-linear function of the state. Examples are provided where the proposed systematic method yields bounds that are tighter or at least not worse than those obtained via standard Lyapunov analysis. We also show how our method can be combined with Lyapunov analysis to improve on the bounds provided by either approach.     

Design of a sliding mode control system for chemical processes

This paper considers the non-linear regulation control of chemical processes. A novel and systematic sliding mode control system design methodology is proposed, which integrates an identified second-order plus dead-time (SOPDT) model, an optimal sliding surface and a delay-ahead predictor. The convergence property of the closed-loop system is guaranteed theoretically by means of satisfying a sliding condition and the control system performance is examined with some typical chemical processes. Besides, with the concept of delay equivalent, the proposed sliding mode control scheme can be utilized directly to the regulation control of a non-minimum phase process. As a special case the proposed scheme is further extended to the control of chemical processes whose dynamics are simply described by a first-order plus dead-time (FOPDT) model. In addition, the decentralized sliding mode control scheme for multivariable processes is also explored in this paper. Extensive simulation results reveal that the proposed sliding mode control system design methodology is applicable and promising for the non-linear regulation of time-delay chemical processes.     

Non-linear output feedback stabilization on a bounded region of attraction

In this paper it is shown that, for multi-input single-output non-affine non-linear systems, when a state feedback control stabilizes an equilibrium point of a plant with a certain bounded region of attraction, it is also stabilized by an output feedback controller with arbitrarily small loss of the region. Moreover, the proposed output feedback controller has the dynamic order n which is the same as the order of the plant. From any given state feedback, an explicit form of the overall controller is provided. A sufficient condition presented for the result is shown to be necessary and sufficient for regional uniform observability when the system is input affine. Thus, the result can be regarded as a regional separation principle for affine non-linear systems.     

Optimal State Estimation and Fault Diagnosis for a Class of Nonlinear Systems

This study proposes a scheme for state estimation and,consequently,fault diagnosis in nonlinear systems.Initially,an optimal nonlinear observer is designed for nonlinear systems subject to an actuator or plant fault.By utilizing Lyapunov's direct method,the observer is proved to be optimal with respect to a performance function,including the magnitude of the observer gain and the convergence time.The observer gain is obtained by using approximation of Hamilton-Jacobi-Bellman(HJB)equation.The approximation is determined via an online trained neural network(NN).Next a class of affine nonlinear systems is considered which is subject to unknown disturbances in addition to fault signals.In this case,for each fault the original system is transformed to a new form in which the proposed optimal observer can be applied for state estimation and fault detection and isolation(FDI).Simulation results of a singlelink flexible joint robot(SLFJR)electric drive system show the effectiveness of the proposed methodology.     

Hybrid dynamical systems with hybrid inputs: Definition of solutions and applications to interconnections

In this paper, we define solutions for hybrid systems with prespecified hybrid inputs. Unlike previous work where solutions and inputs are assumed to be defined on the same domain a priori, we consider the case where intervals of flow and jump times of the input are not necessarily synchronized with those of the state trajectory. This happens in particular when the input is the output of another hybrid system, for instance, in the context of observer design or reference tracking. The proposed approach relies on reparametrizing the jumps of the input in order to write it on a common domain. The solutions then consist of a pair made of the state trajectory and the reparametrized input. Our definition generalizes the notions of solutions of continuous‐time and discrete‐time systems with inputs. We provide an algorithm that automatically performs the construction of solutions for a given hybrid input. In the context of hybrid interconnections, we show how the solutions of the individual systems can be linked to the solutions of a closed‐loop system. Example illustrate the notions and the proposed algorithm.     

一类非完整系统的全局镇定

当非完整系统只能局部转换为链式形式时, 由于存在变换奇异点集合, 针对链式系统所设计的全局反馈控制律只能局部镇定原非完整系统, 而且当期望状态接近奇异点时, 闭环系统的吸引区很小. 本文针对一类可局部转换为链式系统的非完整系统, 首先利用吸引区是状态空间中的一个不变集且与变换奇异点集不相交的条件导出了一个吸引区的不变子集, 然后给出了将系统状态从任意点驱动到吸引区不变子集内的开环控制算法, 最后结合开环控制和闭环控制得到一种混合控制算法. 该混合控制算法可以保证任意不在变换奇异点集合内的期望状态是全局渐近稳定的. 对平面两转动关节空间机器人的仿真结果证实了算法的有效性.     

一类具有饱和发生率的时滞恶意病毒传播模型的分岔控制策略

考虑非线性的饱和发生率,建立一种刻画信息物理融合系统(cyber-physical systems, CPS)中恶意病毒传播的SIRS(susceptible-infected-recovered-susceptible)模型.为了避免因Hopf分岔的产生致使恶意病毒传播扩散,采用参数调节法和状态反馈法相结合的混合分岔控制策略,研究信息物理融合系统的Hopf分岔控制问题,建立受控系统的稳定性条件和分岔判据,探明控制增益参数对Hopf分岔点和分岔极限环幅值的影响规律,并给出分岔阈值与增益参数间的关系图.数值仿真结果表明,所提出的混合分岔控制策略不仅能够改变Hopf分岔点的位置,而且可以有效调节极限环幅值的大小,使得信息物理融合系统产生预期的动力学行为,有效降低恶意病毒传播的危害.     

Oscillation control in non-linear systems using a first-order filter

In this paper we shall address the oscillation control problems in certain classes of non-linear systems whose outputs are required to follow their inputs. It is assumed that the non-linear systems can be well represented by a set of state-space equations and undergo Hopf bifurcation at some particular value of their parameters or their inputs. A simple first-order output feedback controller is proposed for oscillation control in these non-linear systems. First it is shown that in most cases the first-order controller is effective in locally stabilizing a second-order non-linear system which is undergoing Hopf bifurcation. Then a state separation method based on the solution of the associated Riccati equation is applied to the oscillation control of higher-order non-linear systems and a second-order approximated model is developed for the purpose of designing an oscillation controller. The closed-loop stability of the reduced-order model based design is analysed and some sufficient stability conditions are provided. Finally, a detailed application example of a stepper motor is given to show how the controller design method developed in this paper is applied to practical oscillation control problems.     

On the use of parallel processors for implicit Runge-Kutta methods

An iteration scheme, for solving the non-linear equations arising in the implementation of implicit Runge-Kutta methods, is proposed. This scheme is particularly suitable for parallel computation and can be applied to any method which has a coefficient matrixA with all eigenvalues real (and positive). For such methods, the efficiency of a modified Newton scheme may often be improved by the use of a similarity transformation ofA but, even when this is the case, the proposed scheme can have advantages for parallel computation. Numerical results illustrate this. The new scheme converges in a finite number of iterations when applied to linear systems of differential equations, achieving this by using the nilpotency of a strictly lower triangular matrixS ^?1 AS — Λ, with Λ a diagonal matrix. The scheme reduces to the modified Newton scheme whenS ^?1 AS is diagonal.A convergence result is obtained which is applicable to nonlinear stiff systems.     

Emulation of complex open quantum systems using superconducting qubits

With quantum computers being out of reach for now, quantum simulators are alternative devices for efficient and accurate simulation of problems that are challenging to tackle using conventional computers. Quantum simulators are classified into analog and digital, with the possibility of constructing “hybrid” simulators by combining both techniques. Here we focus on analog quantum simulators of open quantum systems and address the limit that they can beat classical computers. In particular, as an example, we discuss simulation of the chlorosome light-harvesting antenna from green sulfur bacteria with over 250 phonon modes coupled to each electronic state. Furthermore, we propose physical setups that can be used to reproduce the quantum dynamics of a standard and multiple-mode Holstein model. The proposed scheme is based on currently available technology of superconducting circuits consist of flux qubits and quantum oscillators.     

A learning approach to tracking in mechanical systems with friction

This paper describes a novel learning control scheme for tracking periodic trajectories in mechanical systems with friction. It is based on the fact that the solution of the closed-loop system tends to be periodic in steady state. When the closed-loop system reaches the steady state, the proposed learning control scheme updates the control input. By doing this iteratively, the proposed learning control scheme eventually can drive the tracking error to zero. Neither the information of the system mass nor the parametric model for friction is required for successful tracking. In particular the proposed learning control scheme can be implemented at cheap cost on a commercially available microprocessor. Furthermore, its generality is well supported through rigorous convergence analysis