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In this work, the problem of designing observers for estimating a single nonlinear functional of the state is formulated for general nonlinear systems. Notions of functional observer linearization are also formulated, in terms achieving exactly linear error dynamics in transformed coordinates and with prescribed rate of decay of the error. Necessary and sufficient conditions for the existence of a lower-order functional observer with linear dynamics are derived. The results provide a direct generalization of Luenberger's linear theory of functional observers to nonlinear systems. [ABSTRACT FROM AUTHOR]

Abstract: This work studies the problem of design of nonlinear observers in the presence of exogenous disturbances. In particular, the present work proposes a systematic design method for nonlinear state and disturbance observers in modular form, consisting of an observer for the disturbance-free part of the system, along with a disturbance observer and a state-estimate corrector. The modular observer is first defined and characterized in a general setting and then, a systematic design method is developed on the basis of exact linearization with eigenvalue assignment. Necessary and sufficient conditions for feasibility of the proposed nonlinear modular observer design are derived. The proposed modular nonlinear observer is tested through simulation studies in an illustrative example involving a biochemical reactor. [Copyright &y& Elsevier]

Abstract: In this paper it is shown that, if a time-varying uncertain system is robustly completely detectable, then there exists an estimator for this system, i.e. the state vector of the system can be estimated asymptotically. If the time-varying uncertain system is robustly completely observable, it is shown that there exists an estimator for this system with assignable rate of convergence of the error. Moreover, specialized constructions are developed for the special class of triangular systems. [Copyright &y& Elsevier]

Abstract: A new systematic framework for nonlinear observer design that allows the concurrent estimation of the process state variables together with key unknown process or sensor disturbances is proposed. The nonlinear observer design problem is addressed within a similar methodological framework as the one introduced in [N. Kazantzis, C. Kravaris, Nonlinear observer design using Lyapunov''s auxiliary theorem, Systems Control Lett. 34 (1998) 241; A.J. Krener, M. Xiao, Nonlinear observer design in the Siegel domain, SIAM J. Control Optim. 41 (2002) 932.] for state estimation purposes only. From a mathematical standpoint, the problem under consideration is addressed through a system of first-order singular PDEs for which a rather general set of solvability conditions is derived. A nonlinear observer is then designed with a state-dependent gain that is computed from the solution of the system of singular PDEs. Under the aforementioned conditions, both state and disturbance estimation errors converge to zero with assignable rates. The convergence properties of the proposed nonlinear observer are tested through simulation studies in an illustrative example involving a biological reactor. [Copyright &y& Elsevier]

Abstract: This work concerns the optimal regulation of single-input–single-output nonminimum-phase nonlinear processes. The problem of calculation of an ISE-optimal, statically equivalent, minimum-phase output for nonminimum-phase compensation is formulated using Hamilton–Jacobi theory and the normal form representation of the nonlinear system. A Newton–Kantorovich iteration is developed for the solution of the pertinent Hamilton–Jacobi equations, which involves solving a Zubov equation at each step of the iteration. The method is applied to the problem of controlling a nonisothermal CSTR with Van de Vusse kinetics, which exhibits nonminimum-phase behaviour. [Copyright &y& Elsevier]

Abstract: A discrete-time, model-based output feedback control structure for nonlinear processes is developed in the present work. The structure makes use of a closed-loop observer, while at the same time it guarantees that the overall feedback controller possesses integral action. An algebraic transformation is applied on the observer states to insure that the input/output gain of the observer matches the model upon which the static state feedback control law is based. The resulting control algorithm is a two-degree-of-freedom control law, in the sense that the output and the set point are processed in different ways. The control structure is shown not only to have the same properties as the standard model-state feedback structure, but also that it emerges from a model algorithmic control framework. Finally, a simulation example using an exothermic CSTR operating at an open-loop unstable steady state is used to evaluate the closed-loop performance of the proposed method. [Copyright &y& Elsevier]

Abstract: Necessary and sufficient conditions for the solution of robust output feedback stabilization (ROFS) problem are given. The obtained results are applied to the problem of Global Identity Observer Design for forward complete systems without inputs. It is shown that a necessary and sufficient condition for the existence of a Global Identity Observer is the existence of an observer Lyapunov function (OLF). [Copyright &y& Elsevier]

Abstract: In this work, a nonlinear output feedback control algorithm is proposed, in the spirit of model-state feedback control. The structure provides state estimates using a process model, the measured output, and the residual between the model output and the measured output. These estimates will track the process states at a rate determined by a set of tunable parameters. An algebraic transformation of the state estimates is incorporated in the control structure to ensure that the input/output gain of the observer matches the model upon which the static state feedback control law is based. The transformed states are then used in the control law. This leads to a controller of minimal order possessing integral action. The control structure is shown to have the same properties as the standard model-state feedback structure. The resulting algorithm is a two-degree of freedom control law, in the sense that the control action is not a function of the error only, but the output and the set point are processed in different ways. Finally, a simulation example using an exothermic CSTR operating at an open-loop unstable steady state is used to demonstrate the closed-loop performance of the proposed method. [Copyright &y& Elsevier]

This work focuses on synthesizing nonlinear decoupling controllers for multivariable nonlinear systems represented by a state-space model, in the presence of deadtimes. The deadtimes appear in both the inputs and the outputs, but not in the states, and are physically associated with sensors and actuators. Simple sufficient conditions for feasibility of closed-loop deadtimes are derived, which rely only on the structural properties of the system. A control law is then derived so that the closed-loop system is input/output linear and decoupled, with deadtimes equal to the smallest ones that satisfy the feasibility conditions. The proposed method is applied to a chemical process. Its performance is evaluated through simulation in the presence of set-point and disturbance changes. [Copyright &y& Elsevier]

Sequential or goal-oriented experimental design methods help achieve the target cheaply and quickly. In this work, we exploit Bayesian Optimization to obtain accurate and reliable static models for physical phenomena in cases where parametric models are unavailable. Our Guided Design of Experiments (G-DoE) workflow is proposed with a purely explorative acquisition function and an empirical stopping criterion. Two stopping criteria are proposed, one that is based on convergence rates of the prediction uncertainty and another that is based on a tolerance limit. Stopping criteria thresholds are established by studying factors like noise level and dimension size and their impact on prediction uncertainty convergence. Furthermore, we compare the G-DoE framework with classical Full Factorial and Response Surface strategies in terms of the suggested number of experiments and corresponding accuracy of fit. The proposed algorithm is tested using a methanol synthesis reaction experiment, a vapor pressure experiment, and a synthetic example. • The G-DoE algorithm can effectively sample from the design space. • G-DoE utilizes GP regression to achieve the modeling targets quickly. • Two empirical stopping criteria are proposed and tested. • Stopping thresholds consider the effect of noise level and dimension size. [ABSTRACT FROM AUTHOR]