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Abstract: In this paper block circulant and block Toeplitz long strings of MIMO systems with finite length are compared with their corresponding infinite-dimensional spatially invariant systems. The focus is on the convergence of the sequence of solutions to the control Riccati equations and the convergence of the sequence of growth bounds of the closed-loop generators. We show that block circulant approximants of infinite-dimensional spatially invariant systems reflect well the LQR behavior of the infinite-dimensional systems. An example of an exponentially stabilizable and exponentially detectable infinite-dimensional system is also considered in this paper. This example shows that the growth bounds of the Toeplitz approximants, as the length of the string increases, and the growth bound of the corresponding infinite-dimensional model, can be significantly different. On the positive side, we give sufficient conditions for the convergence of the growth bounds. [Copyright &y& Elsevier]

Abstract: In this paper we consider a long string of SISO systems which in the limit becomes a scalar infinite spatially invariant system. We compare the LQR control for long-but-finite strings with the LQR control for the corresponding infinite strings. We give analytical and numerical examples where these are quite different and we investigate the cause. In addition, we obtain sufficient conditions for the LQR solutions to be similar as the length of the string increases. [Copyright &y& Elsevier]

Approximations of the globally optimal nonlinear quadratic regulator (NQR) strategy are employed to control the unstable steady state of a continuous stirred tank reactor. It is shown that the proposed approximate NQR controllers can be uniquely determined through solution of Riccati and linear matrix equations and can deliver better dynamic performance than the linear quadratic regulator (LQR) if the process model is proper. Stability, optimality, and constraint satisfaction regions for these controllers are identified. [ABSTRACT FROM AUTHOR]