A new method is proposed for designing controllers with arbitrarily small tracking error for uncertain, mismatched nonlinear systems in the strict feedback form. This method is another "synthetic input technique," similar to backstepping and multiple surface control methods, but with an important addition, 1 low pass filters are included in the design where is the relative degree of the output to be controlled. It is shown that these low pass filters allow a design where the model is not differentiated, thus ending the complexity arising due to the "explosion of terms" that has made other methods difficult to implement in practice. The backstepping approach, while suffering from the problem of "explosion of terms" guarantees boundedness of tracking errors globally; however, the proposed approach, while being simpler to implement, can only guarantee boundedness of tracking error semiglobally, when the nonlinearities in the system are non-Lipschitz.
An important aspect of an Automated Highway System is automatic vehicle following. Automatic Vehicle follower systems must address the problem of string stability, i.e., the problem of spacing error propagation, and in some cases, amplification upstream from one vehicle to another, due to some disturbance at the head of the platoon. An automatic vehicle following controller design that is (asymptotically) stable for one vehicle following another is not necessarily (asymptotically) stable for a string of vehicles. The dynamic coupling between vehicles in such close-formation platoons is a function of the available information (communicated as well as sensed), decentralized feedback control laws and the vehicle spacing policy in use. In the first half of this paper, we develop a framework for establishing conditions for stability of the string in the presence of such dynamic interactions. We then develop a metric for analyzing the performance of a platoon resulting from different vehicle following control algorithms. This metric is the guaranteed rate of attenuation/non-amplification of spacing errors from one vehicle to another. In the latter half of this paper, we outline and analyze various constant spacing vehicle follower algorithms. All these algorithms are analyzed for sensing/actuation lags.
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