In this work modal model predictive control synthesis for control of Kuramoto-Sivashinsky equation with state and input constraints has been developed. The evolution of a linear dissipative PDE is initially given by an abstract evolution equation in an appropriate Hilbert space. Modal decomposition technique is used to decompose the infinite dimensional system into an interconnection of a finite-dimensional (slow) subsystem with an infinite-dimensional (fast) subsystem. The important consequence of such structured dynamics is the notion of decoupled modes which is of paramount importance for the synthesis of a low-order modal model predictive controller (MMPC). The MMPC synthesis is then formulated in a way that the construction of the cost functional accounts only for the weighted evolution of the slow (finite-dimensional) states, while in the state constraints a high-order (finite-dimensional) approximation of the fast states is utilized (,). As an example of the proposed controller synthesis methodology, the optimal stabilization under the presence of input and state constraints of spatially-uniform unstable steady state of Kuramoto-Sivashinsky equation subject to periodic boundary conditions is considered. Simulation results demonstrate successful application of the proposed predictive control technique with infinite-dimensional closed-loop system stability and the state constraint being enforced at a point within the spatial domain.
 L. H. Chen and H. C. Chang, Nonlinear waves on liquid film surface-II. Bifurcation analyses of the long-wave equation, Chemical Engineering Science, vol. 41, pp. 2477-2486, 1986.
 A. Armaou and P. D. Christofides, Feedback control of the Kuramoto-Sivashinsky equation, Physica D., vol. 137, pp. 49-61, 1999.
 P. D. Christofides and A. Armaou, Global stabilization of the Kuramoto-Sivashinsky equation via distributed output feedback control, Syst. & Contr. Lett., vol. 39, pp. 283-294, 2000.
 C. H. Lee and H. T. Tran, Reduced-order-based feedback control of the Kuramoto-Sivashinsky equation, Journal of Computational and Applied Mathematics, vol. 173, pp. 1-19, 2005.
 Dubljevic, S., N. H. El-Farra, P. Mhaskar and P. D. Christofides, Predictive Control of Parabolic PDEs with State and Control Constraints, Inter. J. Rob. & Non. Contr., in press.
 Dubljevic, S., P. Mhaskar, N. H. El-Farra and P. D. Christofides, Predictive Control of Transport-Reaction Processes, Comp. & Chem. Eng., 29, 2335-2345, 2005.