Membrane Computing and Economics: A General View

Three are the points we briefly discuss here: using membrane computing tools for efficient computing/optimization, the possibilities of using “general" membrane computing (P systems using multisets of symbol objects processed by biochemical-like evolution rules) as a framework for modeling economic processes, and the numerical P systems, a class of computing devices explicitly defined with a motivation related to economics. The discussion is rather informal, only pointing out research directions and providing bibliographical information

Numerical P Systems with Thresholds

Numerical P systems are a class of P systems inspired both from the structure of living cells and from economics. In this work, a control of using evolution programs is introduced into numerical P systems: a threshold is considered and a program can be applied only when the values of the variables involved in the production function of the program are greater than/equal to (lower-threshold) or smaller than/equal to (upper-threshold) the threshold. The computational power of numerical P systems with lower-threshold or upper-threshold is investigated. It is proved that numerical P systems with a lower-threshold, with one membrane and linear production functions, working both in the all-parallel mode and in the one-parallel mode are universal. The result is also extended to numerical P systems with an upperthreshold, by proving the equivalence of the numerical P systems with lower- and upper-thresholds

Motion planning and control: a formal methods approach

Control of complex systems satisfying rich temporal specification has become an increasingly important research area in fields such as robotics, control, automotive, and manufacturing. Popular specification languages include temporal logics, such as Linear Temporal Logic (LTL) and Computational Tree Logic (CTL), which extend propositional logic to capture the temporal sequencing of system properties. The focus of this dissertation is on the control of high-dimensional systems and on timed specifications that impose explicit time bounds on the satisfaction of tasks. This work proposes and evaluates methods and algorithms for synthesizing provably correct control policies that deal with the scalability problems. Ideas and tools from formal verification, graph theory, and incremental computing are used to synthesize satisfying control strategies. Finite abstractions of the systems are generated, and then composed with automata encoding the specifications. The first part of this dissertation introduces a sampling-based motion planning algorithm that combines long-term temporal logic goals with short-term reactive requirements. The specification has two parts: (1) a global specification given as an LTL formula over a set of static service requests that occur at the regions of a known environment, and (2) a local specification that requires servicing a set of dynamic requests that can be sensed locally during the execution. The proposed computational framework consists of two main ingredients: (a) an off-line sampling-based algorithm for the construction of a global transition system that contains a path satisfying the LTL formula, and (b) an on-line sampling-based algorithm to generate paths that service the local requests, while making sure that the satisfaction of the global specification is not affected. The second part of the dissertation focuses on stochastic systems with temporal and uncertainty constraints. A specification language called Gaussian Distribution Temporal Logic is introduced as an extension of Boolean logic that incorporates temporal evolution and noise mitigation directly into the task specifications. A sampling-based algorithm to synthesize control policies is presented that generates a transition system in the belief space and uses local feedback controllers to break the curse of history associated with belief space planning. Switching control policies are then computed using a product Markov Decision Process between the transition system and the Rabin automaton encoding the specification.The approach is evaluated in experiments using a camera network and ground robot. The third part of this dissertation focuses on control of multi-vehicle systems with timed specifications and charging constraints. A rich expressivity language called Time Window Temporal Logic (TWTL) that describes time bounded specifications is introduced. The temporal relaxation of TWTL formulae with respect to the deadlines of tasks is also discussed. The key ingredient of the solution is an algorithm to translate a TWTL formula to an annotated finite state automaton that encodes all possible temporal relaxations of the given formula. The annotated automata are composed with transition systems encoding the motion of all vehicles, and with charging models to produce control strategies for all vehicles such that the overall system satisfies the mission specification. The methods are evaluated in simulation and experimental trials with quadrotors and charging stations