In this paper, an event-triggered adaptive dynamic programming (ADP) method is proposed to deal with the H∞ problem unknown and constrained input. Firstly, H∞-constrained regarded as two-player zero-sum game nonquadratic value function. Secondly, we develop Hamilton–Jacobi–Isaacs(HJI) equation, ADP solve HJI which equivalent solving Nash saddle point of game. An event-based single-critic neural...

X iv :m at h/ 05 12 40 7v 2 [ m at h. FA ] 1 8 Ja n 20 06 Notes on Matrix Valued Paraproducts Tao MEI 1 Abstract Denote by Mn the algebra of n×n matrices. We consider the dyadic paraproducts πb associated with Mn valued functions b, and show that the L(Mn) norm of b does not dominate ||πb||L2(l2n)→L2(l2n) uniformly over n. We also consider paraproducts associated with noncommutative martingales...

In this paper we investigate and compare the properties of the semigroup generated by A, and the sequence Ad , n ∈ N, where Ad = (I +A)(I −A)−1. We show that if A and A−1 generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then Ad is power bounded. For analytic semigroups we can prove stronger results. If A is the infinitesimal generator of an analytic semigroup, the...

In this paper we investigate the relation between discrete and continuous operators. More precisely, we investigate the properties of the semigroup generated by A, and the sequence Ad , n ∈ N, where Ad = (I +A)(I −A)−1. We show that if A and A−1 generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then Ad is power bounded. For analytic semigroups we can prove stronger...

We propose a novel recursive design scheme of state observer for lower triangular nonlinear systems. The design begins from the bottom dynamics and propagates to upper dynamics recalling the backstepping scheme for nonlinear control. The proposed class of systems is fairly general since it includes non-uniformly observable or detectable multi-output systems. The error convergence to zero is pro...

We investigate the computable content of the Uniform Boundedness Theorem and of the closely related Banach-Steinhaus Theorem. The Uniform Boundedness Theorem states that a pointwise bounded sequence of bounded linear operators on Banach spaces is also uniformly bounded. But, given the sequence, can we also effectively find the uniform bound? It turns out that the answer depends on how the seque...

We prove decidability of the boundedness problem for monadic least fixed-point recursion based on positive monadic second-order (MSO) formulae over trees. Given an MSO-formula φ(X,x) that is positive in X, it is decidable whether the fixed-point recursion based on φ is spurious over the class of all trees in the sense that there is some uniform finite bound for the number of iterations φ takes ...

We prove that positive solutions of the superlinear Lane–Emden system in a two-dimensional smooth bounded domain are independently exponents system, provided comparable. As consequence, energy is uniformly bounded, crucial information their asymptotic study. In addition, boundedness may fail if not