Unstructured Model Uncertainty Research Articles

Robust Stability of Barrier-Based Model Predictive Control

Conditions for robust input-output stability of barrier-based model predictive control of linear systems with linear and convex nonlinear (hard or soft) constraints are established through the construction of integral quadratic constraints (IQCs). The IQCs can be used to determine sufficient conditions for global closed-loop stability. In particular, conditions for robust stability can be obtained in the presence of unstructured model uncertainty. IQCs with both static and dynamic multipliers are developed and appropriate convex searches for the multipliers are presented. The effectiveness of the robust stability analysis is demonstrated through an illustrative numerical example.

Safety‐constrained robust adaptive control for a class of MIMO non‐linear systems

This study proposes two new safety-constrained robust indirect adaptive control schemes for a class of multi-input multi-output non-linear systems subject to unstructured additive model uncertainties and external disturbances. The controllers are designed using a novel error transformation and a new asymptotically stable closed-loop non-linear error dynamics. The model uncertainties of the actual system are approximated by constructing a neural network-based auxiliary observer dynamics. The weights of the neural network are updated using a robust Lyapunov stable weight update rule. Using the estimation information of model uncertainties, two different asymptotically and finite-time exponentially stable tracking controllers are designed to minimise the error between auxiliary observer states and reference signals. It is proven that the closed-loop states of the actual system will remain bounded by the imposed state constraints and the steady-state tracking error of the system will converge asymptotically (or exponentially in finite time) to a user-defined domain. The beauty of the proposed control designs lies in the fact that they are easy to design and implement, and provide design freedom to impose constraints on an individual component of the system states. The effectiveness of the proposed techniques is shown by controlling a two-link robot manipulator in a constrained environment.

Design of Robust Fractional-Order PID Controller for DC Motor Using the Adjustable Performance Weights in the Weighted-Mixed Sensitivity Problem

This paper deals with the robust series and parallel fractional-order <em>PID</em> synthesis controllers with the automatic selection of the adjustable performance weights, which are given in the weighted-mixed sensitivity problem. The significant contribution of the paper is to achieve the good trade-off between nominal performances and robust stability for DC motor regardless its nonlinear dynamic behavior, the unstructured model uncertainties and the effect of the sensor noises on the feedback control system. The main goal is formulated as the weighted-mixed sensitivity problem with unknown adjustable performance weight. This problem is then solved using an adequate optimization algorithm and its optimal solution leads to determine simultaneously the robust fractional <em>PID</em> controller, which is proposed by the series and the parallel fractional structures, As well as, the obtained optimal solution determines the corresponding adjustable performance weight.<strong><em> </em></strong>The proposed control technique is applied on DC motor where its dynamic behavior is modeled by unstructured multiplicative model uncertainty. The obtained performances are compared in frequency- and time-domains with those given by both integer controllers such classical <em>PID</em> and <em>H<sub>∞</sub> </em>controllers.

Mean‐square error constrained approach to robust stochastic iterative learning control

A Kalman filtering-based robust iterative learning control algorithm is proposed in this study for linear stochastic systems with uncertain dynamics and unknown noise statistics. Firstly, a learning gain matrix is designed for the nominal case by minimising the trace of the mean-square matrix of the input tracking error. Theoretical results show that the proposed algorithm guarantees not only the asymptotic but also monotonic convergence of the input tracking error in the mean-square error sense, especially when random noises are Gaussian distributed the proposed algorithm is further proved to be asymptotically efficient. In addition, a new mean-square error constrained approach is presented in designing the robust learning gain matrix, taking into account model uncertainties. A sufficient condition is provided such that the mean-square matrix of the input tracking error is constrained within a predesigned upper bound which can monotonically converge to zero. Finally, numerical examples considering both structured and unstructured model uncertainties are included to illustrate the effectiveness of the proposed algorithms.

Resilient and Robust Control of Time-Delay Wind Energy Conversion Systems

Wind energy is the fastest growing and the most promising renewable energy resource. High efficiency and reliability are required for wind energy conversion systems (WECSs) to be competitive within the energy market. Difficulties in achieving the maximum level of efficiency in power extraction from the available wind energy resources warrant the collective attention of control and power system engineers. A strong movement toward sustainable energy resources and advances in control system methodologies make previously unattainable levels of efficiency possible. In this paper, we design a general resilient and robust control framework for a time-delay variable speed permanent magnet synchronous generator (PMSG)-based WECS. A linear matrix inequality-based control approach is developed to accommodate the unstructured model uncertainties, L2 type of external disturbances, and time delays in input and state feedback variables. Computer simulation results have shown the efficacy of the proposed approach of achieving asymptotic stability and H∞ performance objectives.

Design New Online Tuning Intelligent Chattering Free Fuzzy Compensator

This research is focused on proposed adaptive fuzzy sliding mode algorithms with the adaptation laws derived in the Lyapunov sense. The stability of the closed-loop system is proved mathematically based on the Lyapunov method. Adaptive MIMO fuzzy compensate fuzzy sliding mode method design a MIMO fuzzy system to compensate for the model uncertainties of the system, and chattering also solved by new adaption method. Since there is no tuning method to adjust the premise part of fuzzy rules so we presented a scheme to online tune consequence part of fuzzy rules. Classical sliding mode control is robust to control model uncertainties and external disturbances. A sliding mode method with a switching control low guarantees the stability of the certain and/or uncertain system, but the addition of the switching control low introduces chattering into the system. One of the main targets in this research to reduce or eliminate chattering is to insert online tuning method. Classical sliding mode control method has difficulty in handling unstructured model uncertainties. One can overcome this problem by combining a sliding mode controller and artificial intelligence (e.g. fuzzy logic). To approximate a time-varying nonlinear dynamic system, a fuzzy system requires a large amount of fuzzy rule base. This large number of fuzzy rules will cause a high computation load. The addition of an adaptive law to a fuzzy sliding mode controller to online tune the parameters of the fuzzy rules in use will ensure a moderate computational load. The adaptive laws in this algorithm are designed based on the Lyapunov stability theorem. Asymptotic stability of the closed loop system is also proved in the sense of Lyapunov. This method is applied to continuum robot manipulator to have the best performance.

Design Minimum Rule-Base Fuzzy Inference Nonlinear Controller for Second Order Nonlinear System

This research is focused on proposed minimum rule base PID computed torque algorithms with application to continuum robot manipulator. The stability of the closed-loop system is proved mathematically based on the Lyapunov method. Classical Computed Torque Controller (CTC) is robust to control model partly uncertainties and external disturbances. This controller is one of the significant nonlinear methodologies; according to the nonlinear dynamic formulation. One of the main targets in this research is increase the robustness based on the artificial intelligence methodology. Classical computed torque control has difficulty in handling unstructured model uncertainties. One can overcome this problem by combining a computed torque controller and artificial intelligence (e.g. fuzzy logic). To approximate a time-varying nonlinear dynamic system, a fuzzy system requires a large amount of fuzzy rule base. This large number of fuzzy rules will cause a high computation load. To reduce the number of rule base this research is focused on the PD like fuzzy plus integral methodology. This method is applied to continuum robot manipulator to have the best performance.

Distributed sensor fault detection and isolation for multimachine power systems

SUMMARYThis paper presents a distributed sensor fault detection and isolation (FDI) scheme for multimachine power systems. Each generator is interconnected with other generators through a transmission network, where the interactions between directly interconnected generators are nonlinear. In the distributed FDI scheme, a local FDI component is designed for each generator excitation system in the power system based on local measurements and certain communicated information from other FDI components associated with generators that are directly interconnected to the local generator. In each FDI component, adaptive thresholds for distributed FDI are derived, ensuring robustness with respect to nonlinear interconnection and unstructured modeling uncertainty under certain conditions. Furthermore, the fault detectability and isolability properties are investigated, characterizing the class of sensor faults that are detectable and isolable by the distributed FDI method. In addition, the stability and learning capability of the local adaptive fault isolation estimators designed for each generator is derived. A simulation example of a two‐machine power system is used to illustrate the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.

Design New Robust Self Tuning Fuzzy Backstopping Methodology

This research is focused on proposed Proportional-Integral (PI) like fuzzy adaptive backstopping fuzzy algorithms based on Proportional- Derivative (PD) fuzzy rule base with the adaptation laws derived in the Lyapunov sense. Adaptive SISO PI like fuzzy adaptive backstopping fuzzy method has two main objectives; the first objective is design a SISO fuzzy system to compensate for the model uncertainties of the system, and the second objective is focused on the design PI like fuzzy controller based on PD method as an adaptive methodology. Classical backstopping control is robust to control model uncertainties and external disturbances and is a main controller in this research. The fuzzy controller is used in this method to system compensation. To increase the robust of this controller adaptive PI like fuzzy controller is introduced and applied to backstopping fuzzy controller. Classical backstopping control method has difficulty in handling unstructured model uncertainties. One can overcome this problem by combining a backstopping controller and artificial intelligence (e.g. fuzzy logic). To approximate a time-varying nonlinear dynamic system, a fuzzy system requires a large amount of fuzzy rule base. This large number of fuzzy rules will cause a high computation load. The addition of an adaptive law to a backstopping fuzzy controller to online tune the coefficients in use will ensure a moderate computational load. The adaptive laws in this algorithm are designed based on the Lyapunov stability theorem. This method is applied to continuum robot manipulator to have the best performance.

On Line Tuning Premise and Consequence FIS Based on Lyaponuv Theory with Application to Continuum Robot

Classical sliding mode controller is robust to model uncertainties and external disturbances. A sliding mode control method with a switching control low guarantees asymptotic stability of the system, but the addition of the switching control law introduces chattering in to the system. One way of attenuating chattering is to insert a saturation function inside of a boundary layer around the sliding surface. Unfortunately, this addition disrupts Lyapunov stability of the closed-loop system. Classical sliding mode control method has difficulty in handling unstructured model uncertainties. One can overcome this problem by combining a sliding mode controller and fuzzy system together. Fuzzy rules allow fuzzy systems to approximate arbitrary continuous functions. To approximate a time-varying nonlinear system, a fuzzy system requires a large amount of fuzzy rules. This large number of fuzzy rules will cause a high computation load. The addition of an adaptive law to a fuzzy sliding mode controller to online tune the parameters of the fuzzy rules in use will ensure a moderate computational load. Refer to this research; tuning methodology can online adjust both the premise and the consequence parts of the fuzzy rules. Since this algorithm for is specifically applied to a robot manipulator.

Robust and resilient state-dependent control of discrete-time nonlinear systems with general performance criteria

A novel state-dependent control approach for discrete-time nonlinear systems with general performance criteria is presented. This controller is robust for unstructured model uncertainties, resilient against bounded feedback control gain perturbations in achieving optimality for general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state-dependent linear matrix inequality (LMI) at each time step, sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this paper unify existing results on nonlinear quadratic regulator, H∞ and positive real control to provide a novel robust control design. The effectiveness of the proposed technique is demonstrated by simulation of the control of inverted pendulum.

Evaluation Performance of IC Engine: Linear Tunable Gain Computed Torque Controller vs. Sliding Mode Controller

Design a nonlinear controller for second order nonlinear uncertain dynamical systems (e.g., internal combustion engine) is one of the most important challenging works. This paper focuses on the comparative study between two important nonlinear controllers namely; computed torque controller (CTC) and sliding mode controller (SMC) and applied to internal combustion (IC) engine in presence of uncertainties. In order to provide high performance nonlinear methodology, sliding mode controller and computed torque controller are selected. Pure SMC and CTC can be used to control of partly known nonlinear dynamic parameters of IC engine. Pure sliding mode controller and computed torque controller have difficulty in handling unstructured model uncertainties. To solve this problem applied linear error-based tuning method to sliding mode controller and computed torque controller for adjusting the sliding surface gain ( ) and linear inner loop gain ( ). Since the sliding surface gain ( ) and linear inner loop gain ( ) are adjusted by linear error-based tuning method. In this research new and new are obtained by the previous and multiple gains updating factor . The results demonstrate that the error-based linear SMC and CTC are model-based controllers which works well in certain and uncertain system. These controllers have acceptable performance in presence of uncertainty.

Performance-Based Adaptive Gradient Descent Optimal Coefficient Fuzzy Sliding Mode Methodology

Design a nonlinear controller for second order nonlinear uncertain dynamical systems is the main challenge in this paper. This paper focuses on the design and analysis of a chattering free Mamdani's fuzzy-based tuning gradient descent optimal error-based fuzzy sliding mode controller for highly nonlinear dynamic six degrees of freedom robot manipulator, in presence of uncertainties. Conversely, pure sliding mode controller is used in many applications; it has two important drawbacks namely; chattering phenomenon and nonlinear equivalent dynamic formulation in uncertain dynamic parameter. In order to solve the uncertain nonlinear dynamic parameters, implement easily and avoid mathematical model base controller, Mamdani's performance/error-based fuzzy logic methodology with two inputs and one output and 49 rules is applied to pure sliding mode controller. Pure sliding mode controller and error-based fuzzy sliding mode controller have difficulty in handling unstructured model uncertainties. To solve this problem applied fuzzy-based tuning method to error-based fuzzy sliding mode controller for adjusting the sliding surface gain. Since the sliding surface gain is adjusted by gradient descent optimization method. Fuzzy-based tuning gradient descent optimal error-based fuzzy sliding mode controller is stable model-free controller which eliminates the chattering phenomenon without to use the boundary layer saturation function. Lyapunov stability is proved in fuzzy-based tuning gradient descent optimal fuzzy sliding mode controller based on switching (sign) function. This controller has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise time=0.8 second, steady state error = 1e-9 and RMS error=1.8e-12).

Distributed fault detection and isolation scheme for abrupt and incipient faults in a class of nonlinear systems

This note developed a distributed fault detection and isolation scheme for a class of large-scale systems in discrete-time framework. The unstructured modeling uncertainty and abrupt and incipient faults are considered in this scheme. By using overlapping decompositions, the large-scale system is decomposed into a set of subsystems which are monitored by a network of local fault detectors (LFDs) and local fault isolation estimators (LFIEs). Specially, the LFIEs, corresponding the faults affecting the common components among different subsystems, may reach a cooperative (or consensus) isolation decision, based on the fact that they can exchange some knowledge about the local information of system by suitable communication links. As a result, for these LFIEs, the capability of isolating faults may be improved. Moreover, the derivation of rigorous analytical results for the detectability and isolability properties of the proposed scheme is given. Simulation results are provided to show the effectiveness of the presented scheme.

Sensor Bias Fault Detection and Isolation in a Class of Nonlinear Uncertain Systems Using Adaptive Estimation

This technical note presents a sensor fault detection and isolation scheme for a class of Lipschitz nonlinear systems with unstructured modeling uncertainty. It significantly extends previous results by considering a class of system nonlinearities which are modeled as functions of the system input and partially measurable state variables. A new sensor fault diagnosis method is developed using adaptive estimation techniques. Adaptive thresholds for fault detection and isolation are derived, and several important properties are investigated, including robustness, stability and learning capability, and fault isolability. A robotic example is used to show the effectiveness of the method.

Robust and Resilient State Dependent Control of Discrete-Time Nonlinear Systems with General Performance Criteria

AbstractA novel state dependent control approach for discrete-time nonlinear systems with general performance criteria is presented. This controller is robust for unstructured model uncertainties, resilient against bounded feedback control gain perturbations in achieving optimality for general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state dependent linear matrix inequality at each time step, sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this paper unify existing results on nonlinear quadratic regulator, H∞ and positive real control to provide a novel robust control design. The effectiveness of the proposed technique is demonstrated by simulation of the control of inverted pendulum.

Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation

This paper presents a fault detection and isolation (FDI) scheme for a class of Lipschitz nonlinear systems with nonlinear and unstructured modeling uncertainty. This significantly extends previous results by considering a more general class of system nonlinearities which are modeled as functions of the system input and partially measurable state variables. A new FDI method is developed using adaptive estimation techniques. The FDI architecture consists of a fault detection estimator and a bank of fault isolation estimators. The fault detectability and isolability conditions, characterizing the class of faults that are detectable and isolable by the proposed scheme, are rigorously established. The fault isolability condition is derived via the so-called fault mismatch functions, which are defined to characterize the mutual difference between pairs of possible faults. A simulation example of a single-link flexible joint robot is used to illustrate the effectiveness of the proposed scheme.

Robust monetary rules under unstructured model uncertainty

This paper revisits a widely adopted approach to robust decision making developed by Hansen and Sargent (2003, 2008)—henceforth HS—and applies it to monetary policy design in the face of model uncertainty. We pay particular attention to two issues: first, we distinguish three possible forms of the implied game between malign nature and the policymaker in the HS procedure each leading to a different robust and approximating equilibria. Second, we impose the zero lower bound (ZLB) constraint on the nominal interest rate. We show that the ZLB constraint has serious consequences for a policymaker pursuing HS-type robustness, especially when accompanied by an inability to commit.

Fault Diagnosis of a Class of Uncertain Nonlinear Systems with Lipschitz Nonlinearities

This paper presents a fault detection and isolation scheme for a class of Lipschitz nonlinear systems with nonlinear and unstructured modeling uncertainty. This significantly extends previous results by considering a more general class of system nonlinearities which are modeled as functions of the system input and partially measurable state variables. A new fault diagnosis method is developed using adaptive estimation techniques. The fault isolability conditions are rigorously established via the use of the so-called fault mismatch functions, which are defined to characterize the mutual difference between pairs of faults.

Robust output-feedback model predictive control for systems with unstructured uncertainty

In this paper, we present novel results that parameterize a broad class of robust output-feedback model predictive control (MPC) policies for discrete-time systems with constraints and unstructured model uncertainty. The MPC policies we consider employ: (i) a linear state estimator, (ii) a pre-determined feedback gain (iii) a set of “tighter constraints” and (iv) a quadratic cost function in the degrees of freedom and the estimated state. Contained within the class, we find both well-known control policies and policies with novel features. The unifying aspect is that all MPC policies within the class satisfy a robust stability test. The robust stability test is suited to synthesis and incorporates a novel linear matrix inequality (LMI) condition which involves the parameters of the cost function. The LMI is shown to always be feasible under an appropriate small-gain condition on the pre-determined feedback gain and the state estimator. Moreover, we show, by means of both theoretical and numerical results, that choosing the cost function parameters subject to the proposed condition often leads to good nominal performance whilst at the same time guaranteeing robust stability.