Alexey N. Zhirabok

Unified Approach to the Problem of Full Decoupling via Output Feedback

Unified approach to the problem of full decoupling via output feedback is considered for the cases of continuoustime and discrete-time nonlinear system models as well as for discrete-event model. The feature of this approach is that it allows obtaining the unique solution of the problem on algorithmic level for all above kinds of the models. Conventional differential geometric and pair algebra of partitions tools are applied as auxiliary ones for providing the calculations in special model cases.

An approach to the analysis of observability and controllability in nonlinear systems via linear methods

Abstract The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuous- and discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the use of relatively simple linear methods which may be supported by existing programming systems, e.g.,Matlab. Sufficient conditions are given for nonlinear unobservability/uncontrollability analysis. To apply these conditions, one isolates the linear part of the system which is checked to be unobservable/uncontrollable and, if the answer is positive, it is examined whether or not existing nonlinear terms violate the unobservability/uncontrollability property.

Algebraic approach for model decomposition: Application to fault detection and isolation in discrete-event systems

Algebraic approach for model decomposition: Application to fault detection and isolation in discrete-event systems This paper presents a constrained decomposition methodology with output injection to obtain decoupled partial models. Measured process outputs and decoupled partial model outputs are used to generate structured residuals for Fault Detection and Isolation (FDI). An algebraic framework is chosen to describe the decomposition method. The constraints of the decomposition ensure that the resulting partial model is decoupled from a given subset of inputs. Set theoretical notions are used to describe the decomposition methodology in the general case. The methodology is then detailed for discrete-event model decomposition using pair algebra concepts, and an extension of the output injection technique is used to relax the conservatism of the decomposition.

Observer based fault diagnosis in thrusters of autonomous underwater vehicle

The problem of fault diagnosis in thrusters of autonomous underwater vehicle is studied. Solution of the problem involves residual generation as a result of mismatch between vehicle behaviour and its reference model behaviour followed by decision making via evaluation of the residual. Sensitivity theory based methods are developed for the design of both residual generator and decision making procedure. These methods are applied to the model of CR-01 autonomous underwater vehicle. Appropriate simulation results are given.

Linear Methods in Observability and Controllability of Nonlinear Systems

Abstract The paper is devoted to the development of approach to analyze observability and controllability of nonlinear dynamic systems by linear methods. The main idea of this approach is as follows: observability (controllability) of the initial nonlinear system linear part is checked and if it is unobservable (uncontrollable), one examines whether or not the nonlinear term violates this conclusion. Sufficient conditions for unobservability and uncontrollability are obtained.

Robust diagnosis of discrete systems with delay: Logic-dynamical approach

The problem of constructing robust (with respect to the uncontrolled disturbances) diagnostic tools for nonlinear time-invariant discrete systems with a single delay is considered. The solution is based on the logical and dynamical approach, which allows one to solve the problem of diagnosis of nonlinear systems by linear methods without sacrificing the solution quality. The robustness of the diagnostic technique is achieved by combining the optimization approach and averaging the residual signal over time. The presentation is illustrated by a case study.

Fault accommodation in discrete - event systems

The problem of fault accommodation in discrete-event systems is considered. Solution of the problem is related to constructing the control law which provides full decoupling with respect to fault effects. Existing conditions are formulated and calculating relations are given for the control law determination.

Disturbance Decoupling in Finite Automata

The paper addresses the disturbance decoupling problem by dynamic measurement feedback for finite automata. The mathematical technique called the pair algebra of partitions is used. The paper gives sufficient solvability conditions and a procedure to construct the required feedback.

Redundancy Relations for the Diagnosis of Hybrid Systems

In the concept of analytical redundancy, the problem of the functional diagnosis of hybrid systems is studied. The solution of this problem assumes checking the redundancy relations between the inputs and outputs of the system. A method for constructing the redundancy relations that includes transformation of the operational and controlling subsystems and then reduction of the operational subsystem to a form without feedbacks is proposed. The problem is solved using the pair algebra of partitions, algebra of functions, and differential-algebraic methods.

Fault Detection in Nonlinear Systems Via Linear Methods

Abstract The problem of robust linear and nonlinear diagnostic observer design is considered. A method is suggested to construct the observers that are disturbance decoupled or have minimal sensitivity to the disturbances. The method is based on a logic-dynamic approach which allows us to consider systems with non-differentiable nonlinearities in the state equations by methods of linear algebra.