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This overview paper reviews numerical methods for solution of optimal control problems in real-time, as they arise in nonlinear model pre-dictive control (NMPC) as well as in moving horizon estimation (MHE). In the first part, we review numerical optimal control solution methods, focussing exclusively on a discrete time setting. We discuss several… (More)

A new algorithm for solving large-scale convex optimization problems with a separable objective function is proposed. The basic idea is to combine three techniques: Lagrangian dual decomposition, excessive gap and smoothing. The main advantage of this algorithm is that it dynamically updates the smoothness parameters which leads to numerically robust… (More)

— We present a code generation strategy for handling long prediction horizons in the context of real-time nonlin-ear model predictive control (NMPC). Existing implementations of fast NMPC algorithms use the real-time iteration (RTI) scheme and a condensing technique to reduce the number of optimization variables. Condensing results in a much smaller, but… (More)

This paper concerns the stability optimization of (parameterized) matrices A(x), a problem typically arising in the design of fixed-order or fixed-structured feedback controllers. It is well known that the minimization of the spectral abscissa function α(A) gives rise to very difficult optimization problems, since α(A) is not everywhere differentiable, and… (More)

This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization problems with DC constraints and prove its convergence. Then we combine the proposed algorithm with a relaxation technique to… (More)