Nonlinear control synthesis by convex optimization

By Stephen Prajna, Pablo A. Parrilo, Anders Rantzer. IEEE Transactions on Automatic Control, 2004

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ℒ︁2‐Gain analysis and control of uncertain nonlinear systems with bounded disturbance inputs (2008, background): “In parallel, for a more restricted class of systems, some researchers have devised a convex formulation for polynomial systems based on the sum of squares (SOS) decomposition [16, 17].”
Stability in the almost everywhere sense: A linear transfer operator approach (2010, background): “This convexity property is exploited in the work of [3] for the design of stabilizing feedback controllers.”
A tutorial on sum of squares techniques for systems analysis (2005, methodology): “Other work in this area includes estimation of the domain of attraction [34], [50], LPV analysis and synthesis [58] and nonlinear synthesis [17], [ 47 ], [46].”
POSITIVE POLYNOMIALS IN SCALAR AND MATRIX VARIABLES, THE SPECTRAL THEOREM AND OPTIMIZATION (2006, methodology): “eralizing the classical Lyapunov function. Unfortunately, no Positivstellensa¨tz technique is known for for ﬁnding V. However, A. Rantzer cleverly introduced a “dual control Lyapunov function” and in [PPR04] showed that it is quite amenable to sum of squares techniques. Another direction gives a gen”
LQR-trees: Feedback Motion Planning via Sums-of-Squares Verification (2010, methodology): “Freely available libraries, including SOSTOOLS (Prajna et al. 2004a) and the Systems Polynomial Optimization Toolbox (Megretski) make performing these computations in MATLAB feasible.”