We propose an efficient algorithm for the optimal control problems (OCPs) of nonlinear switched systems that optimizes input and switching instants simultaneously a given sequence. consider as optimization variables formulate OCP based on direct multiple shooting method. derive linear equation to be solved in Newton’s method Riccati recursion solve efficiently. The computational time proposed s...

We study (extensions of) polymorphic typed lambda calculus from a point of view of how iterative and recursive functions on inductive types are represented. The inductive types can usually be understood as initial algebras in a certain category and then recursion can be defined in terms of iteration. However, in the syntax we often have only weak initiality, which makes the definition of recurs...

There are two well known systems formalizing total recursion beyond primitive recursion (PR), system T by Gödel and system F by Girard and Reynolds. system T defines recursion on typed objects and can construct every function of Heyting arithmetic (HA). System F introduces type variables which can define the recursion of system T. The result is a system as expressive as second-order Heyting ari...

Recursion is a topic of considerable controversy in linguistics, which stems from its varying definitions and its key features, such as its universality, uniqueness to human language, and evolution. Currently, there appear to be at least two common senses of recursion: (1) embeddedness of phrases within other phrases, which entails keeping track of long-distance dependencies among phrases and (...

SQL is the de facto standard language for relational databases and has evolved by introducing new resources and expressive capabilities, such as recursive definitions in queries and views. Recursion was included in the SQL-99 standard, but this approach is limited as only linear recursion is allowed, mutual recursion is not supported, and negation cannot be combined with recursion. In this work...

We give a recursion for the multivariate Rogers-Szegö polynomials, along with another recursive functional equation, and apply them to compute special values. We also consider the sum of all q-multinomial coefficients of some fixed degree and length, and give a recursion for this sum which follows from the recursion of the multivariate Rogers-Szegö polynomials, and generalizes the recursion for...

In software engineering, taking a good election between recursion and iteration is essential because their efficiency and maintenance are different. In fact, developers often need to transform iteration into recursion (e.g., in debugging, to decompose the call graph into iterations); thus, it is quite surprising that there does not exist a public transformation from loops to recursion that hand...

Recursion is a well known concept within computer science and mathematics . In business management it is rarely used explicitly. Counterexamples are applications of dynamic programming and the ́Viable System ́ of Stafford Beer [Beer, 1972]. This paper demonstrates the broad applicability of recursion to managing complexity, especially in business. It starts by showing that recursion is – in cont...

We present BC ε which is a function algebra that is sound and complete for LOGSPACE. It is based on the novel recursion-theoretic principle of generalized recursion where the step length of primitive recursion can be varied at each step. This allows elegant representations of functions like logarithm and division. Unlike characterizations found in the literature, it is noticeable that there doe...

In this paper we study the asymptotic behavior of stochastic approximation schemes with set-valued drift function and non-additive iterate-dependent Markov noise. We show that a linearly interpolated trajectory of such a recursion is an asymptotic pseudotrajectory for the flow of a limiting differential inclusion obtained by averaging the set-valued drift function of the recursion w.r.t. the st...