2022/02/16 by Lars Grüne, Grüne, Lars, Friedrich Philipp +3
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2202.08178
openalex publication_date 2022/02/16 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
We analyze strict dissipativity of generalized linear quadratic optimal control problems on Hilbert spaces. Here, the term ``generalized'' refers to cost functions containing both quadratic and linear terms. We characterize strict pre-dissipativity with a quadratic storage function via coercivity of a particular Lyapunov-like quadratic form. Further, we show that under an additional algebraic assumption, strict pre-dissipativity can be strengthened to strict dissipativity. Last, we relate the obtained characterizations of dissipativity with exponential detectability.