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L2 Gain And Passivity Techniques In Nonlinear Control

(2008). Stochastic Switching Systems: Analysis and Design. Journal of the American Statistical Association: Vol. 103, No. 481, pp. 430-430.

Stochastic Switching Systems: Analysis and Design

Realization of a fractional order fuzzy (FOF) PID controller with nonlinear gains.Performance evaluation of FOFPID controller for a binary distillation column.Comparison of this controller with its integer order counterpart.The proposed FOFPID controller was found superior in all aspects. Expert and intelligent control schemes have recently emerged out as a promising solution with robustness which can efficiently deal with the nonlinearities, along with various types of modelling uncertainties, present in different real world systems e.g. binary distillation column. This paper is an attempt to propose an intelligent control system which takes the form of a fractional order fuzzy proportional-integral-derivative (FOFPID) controller which is investigated as a solution to deal with the complex dynamic nature of the distillation column. The FOFPID controller is an extension of an existing formula based self tuning fuzzy proportional integral controller structure, which varies its gains at run time in accordance with the instantaneous error and rate of change of error. The FOFPID controller is a Takagi-Sugeno (TS) model based fuzzy adaptive controller comprising of non-integer order of integration and differentiation operators used in the controller. It has been observed that inclusion of non-integer order of the integration and differentiation operators made the controller scheme more robust. For the performance evaluation of the proposed scheme, the performance of FOFPID controller is compared with that of its integer order counterpart, a fuzzy proportional-integral-derivative (FPID) controller. The parameters of both the controllers were optimized for minimum integral of absolute error (IAE) using a bio-inspired global optimization algorithm, genetic algorithm (GA). Intensive LabVIEW? simulation studies were performed which included setpoint tracking with and without uncertainties, disturbance rejection, and noise suppression investigations. For testing the parameter uncertainty handling capability of the proposed controller, uncertain and time varying relative volatility and uncertain tray hydraulic constant were applied. Also, for the disturbance rejection studies, intensive simulations were conducted, which included two most common causes of disturbance i.e. variation in feed composition and variation in feed flow rate. All the simulation investigations clearly suggested that FOFPID controller provided superior performance over FPID controller for each case study i.e. setpoint tracking, disturbance rejection, noise suppression and parameter uncertainties.

A fractional order fuzzy PID controller for binary distillation column control

This paper introduces a polynomial fuzzy model (PFM)-based maximum power point tracking (MPPT) control approach to increase the performance and efficiency of the solar photovoltaic (PV) electricity generation The proposed method relies on a polynomial fuzzy modeling, a polynomial parallel distributed compensation, and a sum-of-squares (SOS) decomposition The proposed method is a generalization of the standard Takagi–Sugeno fuzzy models and linear matrix inequality, which showed its effectiveness in decreasing the tracking time and increasing the efficiency of the PV systems In this paper, a direct maximum power (DMP)-based control structure is considered for MPPT Using the PFM representation, the DMP-based control structure is formulated in terms of SOS conditions Unlike the conventional approaches, the proposed approach does not require exploring the maximum power operational point Finally, the extensive studies and hardware-in-the-loop simulations are presented to show the effectiveness of the proposed method

Maximum Power Point Tracking Control of Photovoltaic Systems: A Polynomial Fuzzy Model-Based Approach

An MPC-based power management of standalone DC microgrid with energy storage

In this paper, we will discuss how operational limitations affect input–output behaviours of the system. In particular, we will provide a formulation for passivity and passivity indices of a nonlin...

Passivity and Passivity Indices of Nonlinear Systems Under Operational Limitations using Approximations

This paper deals with the problem of passivity and passivity indices in nonlinear systems. Since the behavior of nonlinear systems depends on the neighborhood of interest, a local approach is taken to study passivity and passivity indices of such systems. An optimization-based method for passivity analysis of nonlinear systems is presented here. The system's dynamics are considered to be defined by polynomial functions, which can cover a broad range of nonlinear systems. Also, state space and input space are considered to be defined as semialgebraic sets. Results are presented as sum of squares optimization, which can directly address nonlinearities without any linearization or further approximation. Examples are given to show the necessity of local analysis for passivity of nonlinear systems and demonstrate the effectiveness of the proposed method.

Local passivity analysis of nonlinear systems: A sum-of-squares optimization approach

This paper presents a new algorithmic method to design PI controller for a general class of nonlinear polynomial systems. Design procedure can take place on certain or uncertain nonlinear model of plant and is based on sum of squares optimization.The so-called density function is employed to formulate the design problem as a convex optimization program in the sum of squares form. Robustness of design is guaranteed by taking parametric uncertainty into account with an approach similar to that of generalized $${\mathcal {S}}$$
 -Procedure. Validity and applicability of the proposed methods are verified via numerical simulations. The method presented here for PI controller design is not based on local linearization and works globally. Derived stability conditions overcome several drawbacks seen in previous results, such as depending on a linearized model or a stable model. Furthermore, employing sum of squares technique makes it possible to derive stability conditions with least conservatism and directly design controller for polynomial affine nonlinear systems.

A sum of squares approach to robust PI controller synthesis for a class of polynomial multi-input multi-output nonlinear systems

Analysis and resilient design of Cyber-physical Systems have greatly benefited from energy based concepts of passivity and dissipativity. Recently, there has been much research devoted to the use of passivity indices in different components of Cyber-physical systems. Passivity indices are measures of passivity, indicating how passive a system is or how far is it from being passive and generalize passivity based methods to systems that might not be passive. In this paper, we will review recent advances in the use of passivity indices in Cyber-physical systems. We will overview how the indices have been defined and applied to different components of Cyber-physical systems and how they are used in the resilient design of compositional Cvber-phvsical systems.

Recent Advances in Analysis and Design of Cyber-physical Systems using Passivity Indices

This paper presents a new data-driven fault identification and controller reconfiguration algorithm. The presented algorithm relies only on the system's input and output data, and it does not require a detailed system description. The proposed algorithm detects changes in the input-output behavior of the system, whether due to faults or malicious attacks and then reacts by reconfiguring the existing controller. This method does not identify the internal structure of the system nor the extent and nature of the attack; hence it can quickly react to faults and attacks. The proposed method can be readily applied to various applications without significant modifications or tuning, as demonstrated by the examples in the paper.

Hasan Zakeri

Papers

Passivity and Passivity Indices of Nonlinear Systems Under Operational Limitations using Approximations

Local passivity analysis of nonlinear systems: A sum-of-squares optimization approach

A sum of squares approach to robust PI controller synthesis for a class of polynomial multi-input multi-output nonlinear systems

Recent Advances in Analysis and Design of Cyber-physical Systems using Passivity Indices

A Data-driven Adaptive Controller Reconfiguration for Fault Mitigation: A Passivity Approach