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The use of a multi-input control design procedure for uncertain nonlinear systems expressible in multi-input parametric-pure feedback form to determine the control law for a class of mechanical systems is described in this paper. The proposed procedure, based on the well-known backstepping design technique, relies on the possibility of extending to multi-input uncertain systems a second order sliding mode control approach recently developed, thus reducing the computational load, as well as increasing...
The implementation of control laws with distributed delays that assign the spectrum of unstable linear multivariable systems with delay in the input requires an approximation of the integral. A necessary condition for stability of the closed-loop system is shown to be the stability of the controller itself. An illustrative multivariable example is given.
Recently, distributed convex optimization has received much attention by many researchers. Current research on this problem mainly focuses on fixed network topologies, without enough attention to switching ones. This paper specially establishes a new technique called averaging-base approach to design a continuous-time distributed algorithm for convex optimization problem under switching topology. This idea of using averaging was proposed in our earlier works for the consensus problem of multi-agent...
The paper consists of two parts. In the first part, new canonical forms are defined for singular 1D linear systems and a procedure to determine nonsingular matrices transforming matrices of singular systems to their canonical forms is derived. In the second part new canonical forms of matrices of the singular 2D Roesser model are defined and a procedure for determining realisations in canonical forms for a given 2D transfer function is presented. Necessary and sufficient conditions for the existence...
In this paper a complete presentation is given of a new canonical representation of multi-input, multi-output linear stochastic systems. Its equivalence with operator form directly linked with ARMA processes as well as with classical state space representation is given, and a transfer matrix interpretation is developed in an example. The importance of the new representation is mainly in the fact that in the joint state and parameters estimation problem, all unknown parameters appear linearly when...
Considering a controllable, square, linear multivariable system, which is decouplable by static state feedback, we completely characterize in this paper the structure of the decoupled closed-loop system. The family of all attainable transfer function matrices for the decoupled closed-loop system is characterized, which also completely establishes all possible combinations of attainable finite pole and zero structures. The set of assignable poles as well as the set of fixed decoupling poles are determined,...
This paper presents an algebraic design theory for interconnected systems. Usual multivariable linear systems are described in a unified way. Both square and nonsquare plants and controllers are included in the study and an easy characterization of the achievable I/O (input-to-output) and D/O (disturbance-to-output) maps is presented through the use of appropriate controllers. Sufficient conditions of stability are given.
The controllability and reconstructability (global) of the system described by a digital N-D Roesser model are defined. Then, necessary and sufficient conditions for system controllability and reconstructability are given. The conditions constitute a generalization of the corresponding conditions for 1-D systems.
We consider linear 2-D systems of Fornasini-Marchesini type in the continuous-time case with non-constant coefficients. Using an explicit representation of the solutions by utilizing the Riemann-kernel of the equation under consideration, we obtain controllability and observability criteria in the case of the inhomogeneous equation, where control is obtained by choosing the inhomogeneity appropriately, but also for the homogeneous equation, where control is obtained by steering with Goursat data....
Local constrained controllability problems for nonlinear finite-dimensional discrete 1-D and 2-D control systems with constant coefficients are formulated and discussed. Using some mapping theorems taken from nonlinear functional analysis and linear approximation methods, sufficient conditions for constrained controllability in bounded domains are derived and proved. The paper extends the controllability conditions with unconstrained controls given in the literature to cover both 1-D and 2-D nonlinear...
A tracking problem is considered in the context of a class of multi-input, multi-output, nonlinear systems modelled by controlled functional differential equations. The class contains, as a prototype, all finite-dimensional, linear, -input, -output, minimum-phase systems with sign-definite “high-frequency gain”. The first control objective is tracking of reference signals by the output of any system in : given , construct a feedback strategy which ensures that, for every (assumed bounded...
A tracking problem is considered
in the context of a class of multi-input,
multi-output, nonlinear systems modelled by controlled functional
differential equations. The class contains, as a prototype, all
finite-dimensional, linear, m-input, m-output, minimum-phase
systems with sign-definite “high-frequency gain". The first control
objective is tracking of reference signals r by the output y of
any system in : given , construct a
feedback strategy which ensures that, for every r (assumed bounded
with...
The paper presents the training problem of a set of neural nets to obtain a (gain-scheduling, adaptive) multivariable neural controller for control of a nonlinear MIMO dynamic process represented by a mathematical model of Low-Frequency (LF) motions of a drillship over the drilling point at the sea bottom. The designed neural controller contains a set of neural nets that determine values of its parameters chosen on the basis of two measured auxiliary signals. These are the ship's current forward...
This paper deals with the direct solution of the pole placement problem by state-derivative feedback for multi- input linear systems. The paper describes the solution of this pole placement problem for any controllable system with nonsingular system matrix and nonzero desired poles. Then closed-loop poles can be placed in order to achieve the desired system performance. The solving procedure results into a formula similar to Ackermann one. Its derivation is based on the transformation of linear...
This paper introduces a complete parametric approach for solving the eigenstructure assignment problem using proportional-plus-derivative feedback for second-order linear control systems. In this work, necessary and sufficient conditions that ensure the solvability for the second-order system are derived. A parametric solution to the feedback gain matrix is introduced that describes the available degrees of freedom offered by the proportional-plus-derivative feedback in selecting the associated...
A new problem of decreasing the degree of the closed-loop characteristic polynomial of the 2D Roesser model by a suitable choice of state feedbacks is formulated. Sufficient conditions are established under which it is possible to choose state feedbacks such that the non-zero closed-loop characteristic polynomial has degree zero. A procedure for computation of the feedback gain matrices is presented and illustrated by a numerical example.
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