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We study the identification of the nonlinearities A,(→)b and c appearing in the quasilinear parabolic equation y_t − div(A(y)∇y + (→)b(y)) + c(y) = u inΩ × (0,T), assuming that the solution of an associated boundary value problem is known at the terminal time, y(x,T), over a (probably small) subset of Ω, for each source term u. Our work can be divided into two parts. Firstly, the uniqueness of A,(→)b and c is proved under appropriate assumptions. Secondly, we consider a finite-dimensional optimization...
For a large class of nonlinear control systems, the main drawback of a semiglobal stabilizing output feedback controllers with increasing regions of attraction is that, when the region of attraction is large, the convergence of solutions of the closed-loop system to the origin becomes slow. To improve the performance of a semiglobal controller, we look for a new feedback control law that preserves the semiglobal stability of the nonlinear system under consideration and that is equal to some...
In this paper, a unified nonlinear modeling and control scheme is presented. A self-structuring Takagi-Sugeno (T-S) fuzzy model is used to approximate the unknown nonlinear plant based on I/O data collected on-line. Both the structure and the parameters of the T-S fuzzy model are updated by an on-line clustering method and a recursive least squares estimation (RLSE) algorithm. The rules of the fuzzy model can be added, replaced or deleted on-line to allow a more flexible and compact model structure....
In this paper we provide a new sufficiency theorem for regular syntheses. The concept of regular synthesis is discussed in [12], where
a sufficiency theorem for finite time syntheses is proved.
There are interesting examples of optimal syntheses that are very regular, but whose trajectories have time domains not necessarily
bounded. The regularity assumptions of the main theorem in [12] are verified by every piecewise smooth feedback control generating
extremal trajectories that reach the target...
The combination of model predictive control based on linear models (MPC) with feedback linearization (FL) has attracted interest for a number of years, giving rise to MPC+FL control schemes. An important advantage of such schemes is that feedback linearizable plants can be controlled with a linear predictive controller with a fixed model. Handling input constraints within such schemes is difficult since simple bound contraints on the input become state dependent because of the nonlinear transformation...
In this paper the classical detection filter design problem is considered as an input reconstruction problem. Input reconstruction is viewed as a dynamic inversion problem. This approach is based on the existence of the left inverse and arrives at detector architectures whose outputs are the fault signals while the inputs are the measured system inputs and outputs and possibly their time derivatives. The paper gives a brief summary of the properties and existence of the inverse for linear and nonlinear...
The concepts of stability, attractivity and asymptotic stability
for systems subject to restrictions of the input values are introduced
and analyzed in terms of Lyapunov functions. A comparison
with the well known input-to-state stability property introduced
by Sontag is provided. We use these concepts in order to derive
sufficient conditions for global stabilization for triangular and
feedforward systems by means of saturated bounded feedback controllers
and also recover some recent results...
The input-output decoupling problem is studied for a class of recursive nonlinear systems (RNSs), i. e. for systems, modelled by higher order nonlinear difference equations, relating the input, the output and a finite number of their time shifts. The solution of the problem via regular static feedback known for discrete-time nonlinear systems in state space form, is extended to RNSs. Necessary and sufficient conditions for local solvability of the problem are proposed. This is the alternative to...
Integrated design of observer based Fault Detection (FD) for a class of uncertain nonlinear systems with Lipschitz nonlinearities is studied. In the context of norm based residual evaluation, the residual generator and evaluator are designed together in an integrated form, and, based on it, a trade-off FD system is finally achieved in the sense that, for a given Fault Detection Rate (FDR), the False Alarm Rate (FAR) is minimized. A numerical example is given to illustrate the effectiveness of the...
A control system is said to be finite if the Lie algebra generated by its vector fields
is finite dimensional. Sufficient conditions for such a system on a compact manifold to be
controllable are stated in terms of its Lie algebra. The proofs make use of the
equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010)
956–973]. and of the existence of an invariant measure on certain compact homogeneous
spaces.
A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.
A control system is said to be finite if the Lie algebra generated by its vector fields
is finite dimensional. Sufficient conditions for such a system on a compact manifold to be
controllable are stated in terms of its Lie algebra. The proofs make use of the
equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010)
956–973]. and of the existence of an invariant measure on certain compact homogeneous
spaces.
The problem of invariant output tracking is considered: given a control system admitting a symmetry group , design a feedback such that the closed-loop system tracks a desired output reference and is invariant under the action of . Invariant output errors are defined as a set of scalar invariants of ; they are calculated with the Cartan moving frame method. It is shown that standard tracking methods based on input-output linearization can be applied to these invariant errors to yield the required...
The problem of invariant output tracking is considered: given a control system
admitting a symmetry group G, design a feedback such that the
closed-loop system tracks a desired output reference and is invariant under the action of G.
Invariant output errors are defined as a set
of scalar invariants of G; they are calculated with the Cartan moving frame
method. It is shown that standard tracking methods based on input-output linearization can be applied to
these invariant errors to yield the...
This paper presents the role of vector relative degree in the
formulation of stationarity conditions of optimal control problems
for affine control systems. After translating the dynamics into a
normal form, we study the Hamiltonian structure. Stationarity
conditions are rewritten with a limited number of variables. The
approach is demonstrated on two and three inputs systems, then, we
prove a formal result in the general case. A mechanical system
example serves as illustration.
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