New approach to robust observer design

This paper shows that based on the recent development of observer design solution, an observer pole selection method can be formulated to minimize the observer gain to the system input. It is proved that this method is a deterministic approach to the recovery of the loop transfer function and robustness of direct state feedback systems.     

Circle-criterion approach to discrete-time nonlinear observer design

This paper addresses the design of discrete-time nonlinear observers through the circle criterion. The new design method is mainly devoted to either globally Lipschitz systems or bounded-state systems whose nonlinearities can be decomposed into a linear combination of positive-slope nonlinearities. The observer design is not restricted to systems with positive-slope nonlinearities, but it encompasses systems with non-positive-slope nonlinearities too. Stability conditions of the observation error are given in terms of numerically tractable linear matrix inequalities. Illustrative examples are presented in order to highlight the main features and advantages of the new proposed technique over some classical designs.     

New approach to observer design for two-dimensional systems

A new method of observer design for shift-invariant two-dimensional digital systems is presented. The method is applicable to a large class of two-dimensional systems and the condition of applicability is very simple to test.     

High-gain observer approach to disturbance attenuation using measurement feedback

A procedure is developed for disturbance attenuation in a linear system via the use of measurement feedback. A high-gain observer is used to recover the disturbance attenuation properties asymptotically, which can be achieved using full state feedback. It is thus shown that the problem of disturbance attenuation via measurement feedback can be decomposed into two problems of disturbance attenuation via state feedback. These problems of disturbance via state feedback can then be solved using existing methods based on the algebraic Riccati equation.     

Discrete-time nonlinear observer design using functional equations

The present research work proposes a new approach to the discrete-time nonlinear observer design problem. Based on the early ideas that influenced the development of the linear Luenberger observer, the proposed approach develops a nonlinear analogue. The formulation of the discrete-time nonlinear observer design problem is realized via a system of first-order linear nonhomogeneous functional equations, and a rather general set of necessary and sufficient conditions for solvability is derived using results from functional equations theory. The solution to the above system of functional equations can be proven to be locally analytic and this enables the development of a series solution method, that is easily programmable with the aid of a symbolic software package.     

Input output linearization approach to state observer design fornonlinear system

Presents a state observer for a class of nonlinear systems based on the input output linearization. While the previous result presented state observers for nonlinear systems of full relative degree, we proposed a procedure fur the design of nonlinear state observers which do not require the hypothesis of full relative degree. Assuming that there exists a global state observer for internal dynamics and that some functions are globally Lipschitz, we can design a globally convergent state observer. It is also shown that if the zero dynamics are locally exponentially stable, then there exists a local state observer. An example is given to illustrate the proposed design of nonlinear state observers     

Stabilizing switching design for switched linear systems: A state-feedback path-wise switching approach

This paper addresses the problem of switching stabilization for discrete-time switched linear systems. Based on the abstraction-aggregation methodology, we propose a state-feedback path-wise switching law, which is a state-feedback concatenation from a finite set of switching paths each defined over a finite time interval. We prove that the set of state-feedback path-wise switching laws is universal in the sense that any stabilizable switched linear system admits a stabilizing switching law in this set. We further develop a computational procedure to calculate a stabilizing switching law in the set.     

A relational algebraic approach to protocol verification

Communications protocols are usually modeled by a pair of finite-state machines that generate the interaction between processes. Protocol verification is a procedure to validate the logical correctness of these interaction sequences and to detect potential design errors. A relational approach is proposed to represent a finite-state machine as a transition table. On this basis, the well-established theory of relational databases can be utilized to derive the global-state transitions of the system. Furthermore, logical errors of a protocol such as deadlocks, incomplete specifications and nonexecutable interactions can be formulated in terms of relational algebra. This approach has been implemented on the INGRES database system and applied to the verification of several protocols     

A frequency domain approach to minimal-order observer design for several linear functions of the state

A design procedure for minimal-order observers which is applicable to linear, observable, time-invariant systems is developed based on certain polynomial matrices associated with the transfer functions of the plant. The approach is to select the observer dynamics so that the feedback control law is satisfied with a minimal-order system. The method is a frequency domain technique but is significantly different from earlier results. Necessary and sufficient conditions for construction of a minimal-order observer to observe several linear functions of the state are given.     

An algebraic approach to the design of compilers for object-oriented languages

In this paper we describe an algebraic approach to construct provably correct compilers for object-oriented languages; this is illustrated for programs written in a language similar to a sequential subset of Java. It includes recursive classes, inheritance, dynamic binding, recursion, type casts and test, assignment, and class-based visibility, but a copy semantics. In our approach, we tackle the problem of compiler correctness by reducing the task of compilation to that of program refinement. Compilation is identified with the reduction of a source program to a normal form that models the execution of object code. The normal form is generated by a series of correctness-preserving transformations that are proved sound from the basic laws of the language; therefore it is correct by construction. The main advantages of our approach are the characterisation of compilation within a uniform framework, where comparisons and translations between semantics are avoided, and the modularity and extensibility of the resulting compiler.     

Controller and observer design for a class of discrete-time nonlinear switching systems

The main contribution of this paper is to present some controller synthesis results for the discrete-time nonlinear (Lipschitz-like) switching systems. Under the assumption that the discrete state of switching systems is known, three related problems are considered, which are full-state feedback controller design, continuous state observer design, and observer-based output feedback controller design. The basic idea of the proposed approaches is to construct the different types of Hybrid Lyapunov function to guarantee the stability, and all of these methods are given in terms of linear matrix inequalities. The results obtained in this paper are only dependent on the Lipschitz-like constant matrices without regard to the specific nonlinear forms. Finally, a numerical example made up of two subsystems is given to show the applicability of theoretical results.     

A block triangular observer form for non-linear observer design

This paper discusses observer design for unforced non-linear multi-output systems using a block triangular observer form (BTOF). The BTOF allows an established exact error linearization observer design method to be generalized to a larger class of multi-output systems. Observer design proceeds in a decentralized manner, or subsystem-at-a-time, starting with the uppermost subsystem. Designs for each subsystem effectively treat upper subsystem states as known measurements and are relatively simple given their reduced dimension. Exponential error stability results are given. New necessary and sufficient existence conditions are given for the BTOF. Examples illustrate the construction of the BTOF coordinates and the advantages of a BTOF-based design compared to a generally applicable method.     

A linear algebraic approach to multisequence shift-register synthesis

An efficient algorithm which synthesizes all shortest linear-feedback shift registers generating K given sequences with possibly different lengths over a field is derived, and its correctness is proved. The proposed algorithm generalizes the Berlekamp-Massey and Feng-Tzeng algorithms and is based on Massey’s ideas. The time complexity of the algorithm is O(KλN) ≲ O(KN ²), where N is the length of a longest sequence and λ is the linear complexity of the sequences.     

A direct decoupling approach for efficient reliability-based design optimization

This paper develops an efficient methodology to perform reliability-based design optimization (RBDO) by decoupling the optimization and reliability analysis iterations that are nested in traditional formulations. This is achieved by approximating the reliability constraints based on the reliability analysis results. The proposed approach does not use inverse first-order reliability analysis as other existing decoupled approaches, but uses direct reliability analysis. This strategy allows a modular approach and the use of more accurate methods, including Monte-Carlo-simulation (MCS)-based methods for highly nonlinear reliability constraints where first-order reliability approximation may not be accurate. The use of simulation-based methods also enables system-level reliability estimates to be included in the RBDO formulation. The efficiency of the proposed RBDO approach is further improved by identifying the potentially active reliability constraints at the beginning of each reliability analysis. A vehicle side impact problem is used to examine the proposed method, and the results show the usefulness of the proposed method.     

A systematic approach to adaptive observer synthesis for nonlinearsystems

Geometric techniques of controller design for nonlinear systems have enjoyed great success. A serious shortcoming, however, has been the need for access to full-state feedback. This paper addresses the issue of state estimation from limited sensor measurements in the presence of parameter uncertainty. An adaptive nonlinear observer is suggested for Lipschitz nonlinear systems, and the stability of this observer is shown to be related to finding solutions to a quadratic inequality involving two variables. A coordinate transformation is used to reformulate this inequality as a linear matrix inequality. A systematic algorithm is presented, which checks for feasibility of a solution to the quadratic inequality and yields an observer whenever the solution is feasible. The state estimation errors then are guaranteed to converge to zero asymptotically. The convergence of the parameters, however, is determined by a persistence-of-excitation-type constraint     

Relaxed observer design of discrete-time nonlinear systems via a novel ranking-based switching mechanism

In this paper, the problem of relaxed observer design of discrete-time nonlinear systems is studied by developing a novel ranking-based switching mechanism. To do this, the useful ranking information of the normalized fuzzy weighting functions is utilized in order to give a denser subdivision of the normalized fuzzy weighting function space and therefore essentially yields the proposed ranking-based switching mechanism. Based on the obtained switching mechanism, a family of switching observers can be developed for the purpose of guaranteeing the estimation error system to be asymptotically stable with less conservatism than the existing results available in the references. Finally, two numerical examples are presented to illustrate the advantages of the proposed method.     

An algebraic approach towards the controllability of controlled switching linear hybrid systems

Based on the hybrid controllability concept (IEEE Automat. Control 43(4) (1998) 491), the controllability problem for a class of hybrid control systems referred to as controlled switching linear hybrid systems is discussed. One sufficient condition and one necessary condition are derived by employing algebraic manipulations of related system matrices. The computational test of these conditions and some examples are also discussed.     

An uncertainty-based approach to discrete-time fault estimation observer design for nonuniformly sampled systems

This paper considers the fault estimation problem of nonuniformly sampled system in which sensor sampling is performed at aperiodic interval. After being discretized at sampling instant, the nonuniformly sampled system is modeled as an equivalent polytopic system with norm bounded uncertainties. A discrete-time time-varying fault estimation observer with multiple design freedom is then constructed, and a sufficient condition given in linear matrix inequality (LMI) is provided to obtain the constant filter gain and ensure not only the asymptotic stability of fault estimation error but also the robustness of uncertainties. Compared with the existing observer designed based on continuous-time delay approach, the proposed one has a better estimation accuracy and less conservatism and is easy for digital implementation. A numerical simulation and a quadruple-tank benchmark are used to demonstrate the effectiveness and superiority of the proposed method.     

A graphical technique for nonlinear algebraic equations

A graphical root-finding procedure is proposed for nonlinear algebraic equations. It employs two graphs of the zero-curves of the real and imaginary parts of the polynomial. It gives information on the approximate location for every root together with its multiplicity on the basis of the argument principle. Locally convergent iterative method for roots may enjoy this information for their implementation. Some numerical examples are shown with the graphs.