This chapter discusses conditions that guarantee that the state of a system is always nonnegative. This property is important because in many applications the state must not be negative. For example, production output, population, armament level, water flow, and so on must always be nonnegative. The chapter discusses the description of a special filter that minimizes the mean square error of the final state. It is devoted to adaptive control systems, where the control is based on continuous measurements of the state and/or output. The chapter outlines the basics of neural networks and neural computing. The field of artificial neural networks is arguably the fastest growing field in artificial intelligence. Neural networks can deal with noisy and imprecise data, learn automatically from training data, adapt to a changing environment, degrade gracefully in the face of component failure, generalize to new situations, and (once trained) execute quickly.