6,025 research outputs found
A weak maximum principle-based approach for input-to-state stability analysis of nonlinear parabolic PDEs with boundary disturbances
In this paper, we introduce a weak maximum principle-based approach to
input-to-state stability (ISS) analysis for certain nonlinear partial
differential equations (PDEs) with boundary disturbances. Based on the weak
maximum principle, a classical result on the maximum estimate of solutions to
linear parabolic PDEs has been extended, which enables the ISS analysis for
certain {}{nonlinear} parabolic PDEs with boundary disturbances. To illustrate
the application of this method, we establish ISS estimates for a linear
reaction-diffusion PDE and a generalized Ginzburg-Landau equation with
{}{mixed} boundary disturbances. Compared to some existing methods, the scheme
proposed in this paper involves less intensive computations and can be applied
to the ISS analysis for a {wide} class of nonlinear PDEs with boundary
disturbances.Comment: 14 page
Constrained optimal control theory for differential linear repetitive processes
Differential repetitive processes are a distinct class of continuous-discrete two-dimensional linear systems of both systems theoretic and applications interest. These processes complete a series of sweeps termed passes through a set of dynamics defined over a finite duration known as the pass length, and once the end is reached the process is reset to its starting position before the next pass begins. Moreover the output or pass profile produced on each pass explicitly contributes to the dynamics of the next one. Applications areas include iterative learning control and iterative solution algorithms, for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modeling of numerous industrial processes such as metal rolling, long-wall cutting, etc. In this paper we develop substantial new results on optimal control of these processes in the presence of constraints where the cost function and constraints are motivated by practical application of iterative learning control to robotic manipulators and other electromechanical systems. The analysis is based on generalizing the well-known maximum and -maximum principles to the
ISS Estimates in the Spatial Sup-Norm for Nonlinear 1-D Parabolic PDEs
This paper provides novel Input-to-State Stability (ISS)-style maximum
principle estimates for classical solutions of highly nonlinear 1-D parabolic
Partial Differential Equations (PDEs). The derivation of the ISS-style maximum
principle estimates is performed by using an ISS Lyapunov Functional for the
sup norm. The estimates provide fading memory ISS estimates in the sup norm of
the state with respect to distributed and boundary inputs. The obtained results
can handle parabolic PDEs with nonlinear and non-local in-domain terms/boundary
conditions. Three illustrative examples show the efficiency of the proposed
methodology for the derivation of ISS estimates in the sup norm of the state.Comment: 20 pages, submitted to ESAIM COCV for possible publicatio
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